Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 35*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 35*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.96 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 30*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 30*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 5.48 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 1*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 1*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.58 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 26*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 26*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.8 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 20*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 20*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 41*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 41*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 4.53 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 38*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 38*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.33 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 44*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 44*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.32 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 11*y'' + 36*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(11*y(t).diff(t, 2) + 36*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.81 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 49*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 49*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.57 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 2*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 2*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.63 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 39*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 39*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.8 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 14*y'' + 36*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(14*y(t).diff(t, 2) + 36*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.6 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 1*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 1*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.29 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 44*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 44*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.1 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 4*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 4*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.41 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 23*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 23*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.4 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 37*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 37*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.72 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 44*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 44*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.83 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 6*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 6*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.56 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 19*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 19*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 5*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 5*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 8*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 8*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.94 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 34*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 34*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 4.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 27*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 27*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.26 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 47*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 47*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.53 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 39*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 39*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.55 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 27*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 27*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.67 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 3*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 3*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.73 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 14*y'' + 24*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(14*y(t).diff(t, 2) + 24*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.31 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 3*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 3*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 15*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 15*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.22 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 8*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 8*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.63 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 8*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 8*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.41 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 50*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 50*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.67 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 49*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 49*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.65 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 6*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 6*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.71 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 28*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 28*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.47 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 25*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 25*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.15 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 12*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 12*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 22*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 22*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.77 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 38*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 38*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.33 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 37*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 37*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 6.08 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 6*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 6*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 12*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 12*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.77 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 35*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 35*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.09 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 17*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 17*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.06 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 34*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 34*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 4.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 33*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 33*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.48 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 27*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 27*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.3 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 44*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 44*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.66 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 16*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 16*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.97 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 42*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 42*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.49 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 19*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 19*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.54 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 12*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 12*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.84 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 31*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 31*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.86 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 33*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 33*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.32 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 24*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 24*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.26 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 47*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 47*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.17 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 49*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 49*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 4.95 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 37*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 37*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.36 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 7*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 7*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.61 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 10*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 10*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.58 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 32*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 32*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.79 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 21*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 21*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.05 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 36*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 36*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 48*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 48*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.63 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 20*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 20*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.05 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 23*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 23*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.6 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 35*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 35*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.36 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 31*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 31*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.24 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 38*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 38*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.76 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 40*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 40*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.83 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 4*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 4*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.41 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 17*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 17*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.92 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 38*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 38*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.5 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 17*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 17*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.3 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 19*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 19*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.97 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 11*y'' + 22*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(11*y(t).diff(t, 2) + 22*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.41 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 44*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 44*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.83 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 6*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 6*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 19*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 19*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.13 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 30*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 30*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 49*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 49*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.65 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 2*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 2*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.5 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 13*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 13*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.55 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 33*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 33*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.17 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 36*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 36*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.73 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 42*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 42*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.29 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 47*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 47*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.57 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 5*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 5*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 47*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 47*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 6.86 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 5*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 5*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.79 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 40*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 40*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 6.32 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 10*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 10*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 15*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 15*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.58 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 14*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 14*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.91 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 44*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 44*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.83 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 8*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 8*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 11*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 11*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.25 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 4*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 4*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.15 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 3*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 3*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.39 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 11*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 11*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.66 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 33*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 33*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.39 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 47*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 47*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 6.86 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 14*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 14*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.18 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 12*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 12*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.82 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 30*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 30*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.94 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 44*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 44*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.48 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 25*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 25*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.25 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 7*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 7*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.88 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 5*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 5*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.79 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 27*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 27*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.64 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 1*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 1*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 34*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 34*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.46 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 34*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 34*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.51 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 11*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 11*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.32 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 4*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 4*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.41 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 3*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 3*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.5 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 2*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 2*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.82 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 12*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 12*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 24*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 24*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.19 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 35*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 35*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.09 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 9*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 9*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.83 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 30*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 30*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.87 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 21*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 21*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.05 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 26*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 26*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.55 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 48*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 48*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 24*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 24*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.83 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 8*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 8*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.07 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 28*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 28*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.65 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 45*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 45*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.94 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 50*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 50*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.36 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 16*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 16*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.63 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 25*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 25*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.5 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 20*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 20*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 32*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 32*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.83 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 34*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 34*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.62 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 6*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 6*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.87 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 36*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 36*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.5 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 14*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 14*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.53 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 25*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 25*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.89 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 14*y'' + 19*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(14*y(t).diff(t, 2) + 19*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.16 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 9*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 9*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.34 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 29*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 29*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.2 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 41*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 41*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.51 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 36*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 36*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.41 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 23*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 23*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.6 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 10*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 10*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.2 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 50*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 50*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.5 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 39*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 39*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.08 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 11*y'' + 1*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(11*y(t).diff(t, 2) + 1*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.3 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 44*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 44*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.32 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 45*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 45*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.54 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 47*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 47*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.9 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 49*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 49*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 4.95 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 50*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 50*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.04 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 49*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 49*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 4.04 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 50*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 50*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.62 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 6*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 6*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 15*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 15*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 15*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 15*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.22 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 32*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 32*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 5.66 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 38*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 38*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.05 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 27*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 27*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.32 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 14*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 14*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.32 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 2*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 2*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.33 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 1*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 1*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.71 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 8*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 8*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.89 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 21*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 21*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.62 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 5*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 5*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.29 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 6*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 6*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.61 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 3*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 3*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.43 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 6*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 6*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.93 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 13*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 13*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.55 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 18*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 18*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 47*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 47*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.57 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 45*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 45*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.54 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 9*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 9*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 26*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 26*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.8 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 22*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 22*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.56 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 28*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 28*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.65 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 36*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 36*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.66 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 32*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 32*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.27 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 27*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 27*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.19 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 35*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 35*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.39 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 17*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 17*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.06 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 28*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 28*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.65 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 14*y'' + 50*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(14*y(t).diff(t, 2) + 50*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.89 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 1*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 1*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.22 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 11*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 11*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.48 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 1*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 1*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.71 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 30*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 30*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.94 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 14*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 14*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.18 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 36*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 36*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.68 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 3*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 3*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.61 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 36*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 36*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.41 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 48*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 48*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.73 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 9*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 9*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.87 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 16*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 16*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.83 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 15*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 15*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.37 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 7*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 7*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.73 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 1*y'' + 4*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(1*y(t).diff(t, 2) + 4*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 11*y'' + 34*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(11*y(t).diff(t, 2) + 34*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.76 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 37*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 37*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.52 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 46*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 46*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.88 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 5*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 5*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.85 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 31*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 31*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.24 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 13*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 13*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.27 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 19*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 19*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.78 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 25*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 25*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.29 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 22*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 22*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.3 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 11*y'' + 20*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(11*y(t).diff(t, 2) + 20*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.35 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 32*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 32*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.53 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 37*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 37*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.43 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 23*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 23*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.4 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 7*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 7*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 25*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 25*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 45*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 45*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 11*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 11*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.86 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 3*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 3*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.22 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 43*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 43*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.89 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 41*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 41*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.42 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 32*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 32*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.63 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 16*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 16*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.97 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 19*y'' + 10*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(19*y(t).diff(t, 2) + 10*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.73 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 3*y'' + 29*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(3*y(t).diff(t, 2) + 29*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.11 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 14*y'' + 42*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(14*y(t).diff(t, 2) + 42*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.73 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 38*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 38*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.52 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 22*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 22*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.05 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 2*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 2*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.35 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 37*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 37*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.72 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 31*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 31*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.1 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 15*y'' + 10*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(15*y(t).diff(t, 2) + 10*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.82 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 25*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 25*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.5 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 33*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 33*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.39 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 20*y'' + 36*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(20*y(t).diff(t, 2) + 36*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.34 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 14*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 14*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.18 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 11*y'' + 21*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(11*y(t).diff(t, 2) + 21*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.38 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 2*y'' + 22*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(2*y(t).diff(t, 2) + 22*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.32 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 42*y' + 9*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 42*y(t).diff(t) + 9*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.87 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 16*y'' + 15*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(16*y(t).diff(t, 2) + 15*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.97 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 17*y'' + 47*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(17*y(t).diff(t, 2) + 47*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.66 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 5*y'' + 38*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(5*y(t).diff(t, 2) + 38*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.76 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 50*y' + 8*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 50*y(t).diff(t) + 8*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 3.54 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 6*y'' + 36*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(6*y(t).diff(t, 2) + 36*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.45 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 9*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 9*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.0 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 12*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 12*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.22 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 7*y'' + 9*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(7*y(t).diff(t, 2) + 9*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.13 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 13*y'' + 32*y' + 4*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(13*y(t).diff(t, 2) + 32*y(t).diff(t) + 4*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.57 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 25*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 25*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.67 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 14*y'' + 26*y' + 10*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(14*y(t).diff(t, 2) + 26*y(t).diff(t) + 10*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.36 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 4*y'' + 18*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(4*y(t).diff(t, 2) + 18*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 47*y' + 1*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 47*y(t).diff(t) + 1*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.17 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 18*y'' + 33*y' + 5*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(18*y(t).diff(t, 2) + 33*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.35 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 41*y' + 2*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 41*y(t).diff(t) + 2*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.85 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 10*y'' + 45*y' + 7*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(10*y(t).diff(t, 2) + 45*y(t).diff(t) + 7*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 2.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 12*y'' + 15*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(12*y(t).diff(t, 2) + 15*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.12 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 9*y'' + 3*y' + 6*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(9*y(t).diff(t, 2) + 3*y(t).diff(t) + 6*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 0.58 rad/s


Instruction: Resoudre l equation differentielle d un oscillateur amorti 8*y'' + 21*y' + 3*y = 0 avec SymPy.

Output:
import sympy as sp
t = sp.Symbol('t', real=True, positive=True)
y = sp.Function('y')
eq = sp.Eq(8*y(t).diff(t, 2) + 21*y(t).diff(t) + 3*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(f"Solution analytique: {sol}")
# Frequence propre quasi-harmonique: omega0 = 1.62 rad/s