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Question: <p>Why are differential equations called differential equations?</p>
Answer: <p>Because they are equations (with the variable being a function, not a number) that involve a function and its derivatives (the functions obtained by differentiating it).</p>
| https://math.stackexchange.com/questions/4631/why-are-differential-equations-called-differential-equations |
Question: <p>Which of these books, Coddington's An Introduction to Differential Equations, Tenenbaum's Ordinary Differential Equations and Ince's Ordinary Differential Equations, is better to learn Differential Equations (at least the ordinary differential equations)?</p>
Answer: <p>Zill & Wright's book "Diff... | https://math.stackexchange.com/questions/3539971/coddingtons-an-introduction-to-differential-equations-tenenbaums-ordinary-dif |
Question: <p>My objective is to study Ordinary and Partial Differential Equations in a theoretical way.
I have 2 options on buying differential equations books in mind. These options are: (1) Differential Equations and Their Applications by Martin Braun and (2) Ordinary Differential Equations by V. I. Arnold plus Part... | https://math.stackexchange.com/questions/3540034/martin-brauns-differential-equations-and-their-applications-or-arnolds-ordinar |
Question: <p>I've seen how one can transform a higher order ordinary differential equation into a system of first-order differential equations, but I haven't been able to find the converse. Is it true that one can transform any system into a higher-order differential equation? If so, is there a general method to do so?... | https://math.stackexchange.com/questions/391002/systems-of-differential-equations-and-higher-order-differential-equations |
Question: <p>I have become a TA for a professor who teaches differential equations. The course is basically a self study course where students are to use their previous knowledge to explore and teach themselves differential equations. There is no book for the class which makes this hard for some students. I am reaching... | https://math.stackexchange.com/questions/3356898/differential-equations-self-study |
Question: <p>I've always wondered why does the differential equation notation for linear equations differ from the standard terminology of vector spaces.</p>
<p>We all know that the equation $y'' + p(x) y' + q(x)y = g(x)$ for some function $g$ is called <em>linear</em> and that the associated equation $y&#... | https://math.stackexchange.com/questions/108544/differential-equations-notation |
Question: <p>Please tell how one can identify 1st order</p>
<p>1) Homogeneous differential equations.</p>
<p>2) Homogeneous linear differential equations.</p>
<p>3) Non Homogeneous differential equations.</p>
<p>4) Non Homogeneous linear differential equations.</p>
Answer: <ul>
<li>First-order means the highest de... | https://math.stackexchange.com/questions/2201171/first-order-ordinary-differential-equations |
Question: <p>I'm just getting into differential equations now and I've got to show that the given $y(x)$ is a solution to the differential equation: $$u'+u = 0 \ , \ y(x) = Ce^{-x}$$</p>
<p>How do I tackle this? I know nothing about differential equations and my book has the strangest explanations.</p>
Answer: <p>The... | https://math.stackexchange.com/questions/723964/getting-into-differential-equations |
Question: <p>Is there a universally recognized term for ODEs considered in the sense of distributions used to describe impulsive/discontinuous processes? I noticed that some authors call such ODEs "measure differential equations" while others use the term "differential equations in distributions". But I don't see a maj... | https://math.stackexchange.com/questions/294696/distinction-between-measure-differential-equations-and-differential-equations |
Question: <p>I am currently taking an Engineering course (differential equations), in which the concept of "Residue" has been introduced. Having missed part of the lecture, and reviewed both the class textbook (no help) and my Anton Bivens Calculus book, I have found almost no information on how to actually calculate t... | https://math.stackexchange.com/questions/82304/differential-equations-residue |
Question: <p>I have been doing some self-study of differential equations and have finished Habermans' elementary text on linear ordinary differential equations and about half of Strogatz's nonlinear differential equations book. The thing that I am noticing is just how much these text avoid engaging the underlying diffe... | https://math.stackexchange.com/questions/3374801/book-recommendation-differential-equations-with-differential-geometry |
Question: <p>How would I solve these differential equations? Thanks so much for the help!</p>
<p>$$P'_0(t) = \alpha P_1(t) - \beta P_0(t)$$
$$P'_1(t) = \beta P_0(t) - \alpha P_1(t)$$</p>
<p>We also know $P_0(t)+P_1(t)=1$</p>
Answer: <p>Note that from the equation you have $$P'_0(t) = \alpha P_1(t) - \bet... | https://math.stackexchange.com/questions/27896/differential-equations |
Question: <h2>Background</h2>
<p>I'm under the impression that a differential equation has locality hardwired into it (which is why we see them more in physics). However, if I wanted to write something non-local I'd use a functional equation. I am aware there are cases where the differential equation has a functional ... | https://math.stackexchange.com/questions/3350892/functional-vs-differential-equations |
Question: <p>Can we solve 1st order q-differential equations using the usual methods of 1st order differential equations? For example, can we use integration factor method to solve this q-differential equations?</p>
<p><span class="math-container">$$\text D_qy(x)=a(x)y(qx)+b(x)$$</span></p>
Answer: <p>Here is how to g... | https://math.stackexchange.com/questions/4324810/1st-order-q-differential-equations |
Question: <p>When I first encountered differential equations,solving them seemed to be somewhat mechanical and I could not enjoy any taste of it.But after undergoing linear algebra course,I think there is more to understand in it rather that differentiating and integrating.I now want to revisit differential equation ag... | https://math.stackexchange.com/questions/3452685/differential-equations-viewed-rigorously |
Question: <p>I've seen questions on what are some good differential equations textbook and people generally points to Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard and so on</p>
<p>I was wondering if there are any free (GNU free documentation license, CC, or alike) textbooks on the subject. A g... | https://math.stackexchange.com/questions/279835/free-differential-equations-textbook |
Question: <p>Often when you study differential equations, you find phenomena in nature modeled by those equations. Sometimes an insight into a physical problem can help you to solve a differential equation. My question is: If you are a pure mathematician studying differential equations, do you have to be good at physic... | https://math.stackexchange.com/questions/590296/differential-equations-and-physical-intuition |
Question: <p>Can someone please clarify what the difference (no pun intended) between the two is? </p>
<p>I am reading <a href="http://www.emis.de/journals/RSMT/RSMT/63-3/197.pdf" rel="nofollow" title="this"><em>this</em></a> tutorial and at the very start they state that a differential inclusion is a solution to</p>
... | https://math.stackexchange.com/questions/1334904/differential-inclusions-vs-differential-equations |
Question: <p>We have that system of differential equations: <span class="math-container">$$
\left\{
\begin{array}{ll}
x'=-x \\
y'=-2y \\
\end{array}
\right.
$$</span>
I have to solve that system but I only know the method of derive first equation and substitute in the second and get a second order differential equa... | https://math.stackexchange.com/questions/3265116/differential-equations-systems |
Question: <p>In every book of the ordinary differential equations that i have it is given existence and uniqueness theory of ordinary differential equations locally i.e. existence of solution in some neighbourhood of the given point. I am searching results and theorems regarding globally existence of solutions of ordin... | https://math.stackexchange.com/questions/3143493/books-for-ordinary-differential-equations |
Question: <p>First of all, please do excuse the lack of correct terminology, I've haven't learnt Differential Equations at school (yet) so this question comes from just a bit of research I did for my own enjoyment.</p>
<p>I was reading up on differential equations and the first thing I read was that their result is ei... | https://math.stackexchange.com/questions/577488/what-comes-after-differential-equations |
Question: <p>I am planning to take Differential equations next semester, but due to a timetable issue I want to study most of it this summer in my spare time to make it easier.</p>
<p>These are the Topics that will be included, which I think represent about half of the Differential equations in other universities:</p>... | https://math.stackexchange.com/questions/2784205/recommended-books-for-differential-equations |
Question: <p>I have the following differential equations, for modeling predator-prey relationships:</p>
<p>$$\frac{dx}{dt} = Ax - Bxy$$
$$\frac{dy}{dt} = Cxy - Dy$$</p>
<p>Where A, B, C, and D are constants. How could I go about solving this? I've only really worked with basic first order differential equations befor... | https://math.stackexchange.com/questions/1676569/solving-coupled-differential-equations |
Question: <p>I have no knowledge of differential equations, but I have the background in differential geometry/topology and analysis that one acquires in a PhD program. I.e. I have a foundational knowledge of Lie groups (roughly equivalent to Knapp's book), Riemannian geometry (roughly equivalent to do Carmo's book) an... | https://math.stackexchange.com/questions/2022841/differential-equations-book |
Question: <p>I intend to take this course named "Differential Equations" and per the department followings contents will be taught</p>
<pre><code>* First Order Differential Equations
* Second Order Linear Equations
* Series Solutions of Second Order Linear Equations
* Higher Order Linear Equations
* The Laplace Trans... | https://math.stackexchange.com/questions/41051/things-i-must-know-before-taking-differential-equations-course |
Question: <p>I was revising differential equations and came across the topic of exact differential equations. I have a doubt concerning it. Suppose the differential equation $M(x,y)dx + N(x,y)dy=0$ is exact. Then the solution is given by:
$\int Mdx +\int (N-\frac{\partial}{\partial y}\int Mdx)dy = c$. I understand that... | https://math.stackexchange.com/questions/51458/exact-differential-equations |
Question: <p>I need to solve this differential equation $$(2x+y)dx + (x-2y)dy=0$$ as an exact differential equation and I know it's exact because I solve the equaliy $$ \frac{\partial(2x+y)}{\partial y} = 1$$ and $$\frac{\partial(x-2y)}{\partial x} = 1$$ so following the steps to solve this kind of equations i have:
$... | https://math.stackexchange.com/questions/1424768/help-differential-equations |
Question: <p>I am reading Ringstrom's book <em>The Cauchy problem in General Relativity</em>, But I don't really understand Chapter 12 associating to tensor equations. I want to read some other material about this. Could anyone suggest me some books about tensor differential equations?</p>
<p>I want to learn something... | https://math.stackexchange.com/questions/739261/tensor-differential-equations |
Question: <p>Consider the vector differential equations
\begin{equation}
\mathbf{x}^{\prime}=\mathbf{A}(t)\cdot\mathbf{x}\tag{1}
\end{equation}
and
\begin{equation}
\mathbf{y}^{\prime}=-\mathbf{A}^{\ast}(t)\cdot\mathbf{y},\tag{2}
\end{equation}
where $\mathbf{A}^{\ast}$ is the complex conjugate transpose of $\mathbf{A}... | https://math.stackexchange.com/questions/2083209/adjoint-differential-equations |
Question: <p>I'm in need of a textbook/workbook that covers differential equations with plenty of practice questions and exercises.
A textbook with a particular focus on Nonlinear Ordinary Differential Equations and Dynamical Systems would be great.</p>
<p>Thanks</p>
Answer: | https://math.stackexchange.com/questions/2215194/textbook-recommendation-for-differential-equations |
Question: <p>I have following three equations $$ u'' - 2u = -2v$$ $$ u(0)=0 $$ $$ u'(1)=0 $$
and from these 3 equations I am trying to find u(v). </p>
<p>It looks to me "Cauchy-Euler Differential Equations - Nonhomogeneous case" but I am not sure about that because it is not an exactly Cauchy form. Could you help me t... | https://math.stackexchange.com/questions/1554087/euler-differential-equations |
Question: <p>I'm new to solving differential equations.</p>
<p>How would we go about solving a differential equation like</p>
<p><span class="math-container">$y'=-4+5y-y^2$</span> ?</p>
Answer: <p><span class="math-container">$$\frac{dy}{dt} = -4+5y-y^2$$</span></p>
<p><span class="math-container">$$\frac{dy}{-4+5y-... | https://math.stackexchange.com/questions/3997332/solving-differential-equations-w-polynomials |
Question: <p>I am trying to get a better understanding of the terminology of differential equations. As I understand it, I can characterize differential equations along different categories:</p>
<p>(i) linear vs. nonlinear
(ii) separable vs. nonseparable
(iii) homogeneous vs. inhomogeneous
(iv) ordinary vs. partial</p... | https://math.stackexchange.com/questions/2051288/terminology-of-differential-equations |
Question: <p>How does distribution theory plays role in solving differential equations?
This question might seem to be very general. I will try to explain, please bear with me.</p>
<p>I understand, distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense and any l... | https://math.stackexchange.com/questions/1177480/distribution-theory-and-differential-equations |
Question: <p>Consider a differential equation with a term containing $y(x_0)$, for example $$y'' - 2y' + y = y(x_0)$$ $x_0 \in \mathbb{R}$ is a constant. My question is, does such equations fall under the category of differential equations? I have never studied any equation with such a term. If its a differential equa... | https://math.stackexchange.com/questions/2879351/can-these-equations-be-considered-as-differential-equations |
Question: <p>I am having a difficulty in deriving stochastic differential equations from geometric Brownian motion dynamics.</p>
<p>Assume S follows the geometric Brownian motion dynamics, dS = μSdt + σSdZ, with μ and σ constants.
Derive the stochastic differential equation satisfied by
y = 2S, y = S^2, y=e^S</p>
<p>... | https://math.stackexchange.com/questions/2370518/deriving-stochastic-differential-equations |
Question: <p>What are the prereqs for differential equations? Do you need to know integral calculus too, and if so, to what extent? I want to learn about DE's as quick as possible but I'm not sure if I'm ready yet, my differential calculus is up to par I believe but my integral calculus is pretty weak, is that going to... | https://math.stackexchange.com/questions/247282/differential-equations-background |
Question: <p>I am learning how to solve differential equations (ordinary and partial)and why they are so important for physics.One thing I have noticed so far is that we know so little on the nature of the solutions of a differential equation , only very few forms of differential equations are solvable and even less fo... | https://math.stackexchange.com/questions/4654977/linearity-of-system-of-differential-equations |
Question: <p>I remember noting from an algebra class that $x$ and $y$ of a linear equation neither divide or multiply with each other which is somewhat clear from the forms of linear equations:</p>
<p>General form of linear equation:</p>
<p>$Ax + By + C = 0$</p>
<p>Slope intercept form:</p>
<p>$y = mx + b$</p>
<p>... | https://math.stackexchange.com/questions/1420439/linear-equation-and-linear-differential-equations |
Question: <p>So this problem may be really simple and there's one small thing I'm missing, but I'm just stumped. </p>
<p>Find 4 solutions of the ODE
$$y^{(4)} − 4 = 0$$
by transforming the ODE into a system of 4 first order differential equations.</p>
<p>I've had no problem solving similar equations, but the lack of ... | https://math.stackexchange.com/questions/2532783/transform-differential-equation-to-system-of-differential-equations |
Question: <p>I have a question about logistic equations in differential equations and setting up the problem accordingly. This was the question presented:</p>
<blockquote>
<p>The number $N(t)$ of people in a community who are exposed to a particular advertisement is governed by the logistic equation. Initially, $N(0... | https://math.stackexchange.com/questions/1502909/logistic-equation-differential-equations |
Question: <p>I've read that the Einstein equation is a set of 10 coupled partial differential equations. I know what a partial differential equation is, but I don't know what a set of coupled partial differential equations is. Please shed some light into this question.</p>
Answer: <p>A set of equations like
$$\frac{\p... | https://math.stackexchange.com/questions/1653992/set-of-coupled-partial-differential-equations |
Question: <p>I have an iterative method of solving differential equations. I would like to emphasize that the method returns <strong>approximate solutions</strong> of differential equations. How should I call this method? I have the following ideas:</p>
<ol>
<li>An iterative approximate method of solving differential ... | https://math.stackexchange.com/questions/2419031/a-method-of-solving-differential-equations-terminology |
Question: <p>hello everyone I have trouble understanding differential equations, am in the second year of studying programing engineer this semester I have differential equations, and my level in math is so low am trying to do my best so my question is what subject should I understand before taking a differential equat... | https://math.stackexchange.com/questions/4247702/how-to-start-studing-differential-equations |
Question: <p>I am interested in systems of differential-algebraic equations (DAE), i.e., systems of equations of the following form
<span class="math-container">$$\dot{x} = f(x,y,t)\\0 = g(x,y,t)$$</span></p>
<p>I am confused about their relation to ordinary differential equations (ODE):
Are there functions that can b... | https://math.stackexchange.com/questions/3571788/are-differential-algebraic-equations-more-expressive-than-ordinary-differential |
Question: <p>While going over problems in differential equations and difference equations, I realized that most of the techniques that we use to solve them are very similar. This has led me to wonder - is there a deeper theory that unifies both of them?</p>
<p>I tried to look around, and all that I could find is somet... | https://math.stackexchange.com/questions/3254891/relation-between-differential-equations-and-difference-equations |
Question: <p>I have many questions I'd like to ask today. I'm currently studying for my A-levels which is a qualification mainly based in England. I'm taking A-level Further Maths, which involves the study of First and Second Order Differential Equations. It seems we are just being taught to apply recipes to these type... | https://math.stackexchange.com/questions/2253813/differential-equations-recipes |
Question: <p>I am an engineer who uses mathematics for applications. I have learnt how to solve differential equations, both ordinary and partial. My impression has been that solving differential equations is all about knowing a bag of diverse tricks: separation of variables, reduction in order, power series method, et... | https://math.stackexchange.com/questions/2422800/single-approach-to-solving-differential-equations |
Question: <p>I have encountered a 2-dimensional system of differential equations. One of them is a <a href="https://en.wikipedia.org/wiki/Delay_differential_equation" rel="nofollow noreferrer">delay differential equation</a> (DDE). Can anybody explain to me how to analyze the stability of a DDE? </p>
Answer: <p>In a n... | https://math.stackexchange.com/questions/2768028/stability-of-delay-differential-equations |
Question: <p>Is the solution to differential equations using power series applicable only to homogeneous differential equations?
I mean equations of the form: <span class="math-container">$$a_2 \phi ''(x)+a_1 \phi '(x)+ \phi(x) = 0$$</span></p>
Answer: <p>If you have a source term <span class="math-container">$f$</spa... | https://math.stackexchange.com/questions/3890164/power-series-solution-for-differential-equations |
Question: <p>In many talks, I have heard people say that the differential equation they are interested in has no analytical solution. Do they really mean that? That is:</p>
<blockquote>
<p>Can you prove a differential equation has no analytical solution? </p>
</blockquote>
<p>I suspect what they mean is that no one... | https://math.stackexchange.com/questions/210346/differential-equations-without-analytical-solutions |
Question: <p>I'm trying to solve the SIR model differential equations by separation of variables to get $S$,$I$,$R$ as functions of time , for example $I$ solved the Infected differential equation as follows:
$$
dI/dt= BIS-YI, \\
dI/dt = I(BS-Y), \\
dI/I= BS-Y dt, \\
\int dI/I = \int (BS-Y) \, dt = \ln{I} = BSt-Yt... | https://math.stackexchange.com/questions/2834514/sir-model-differential-equations |
Question: <p>I want to solve the two following differential equations:</p>
<p>(1) $ f''(t) = 3f'(t) - f(t)$</p>
<p>(2) $ f''(t) = 2f'(t) - f(t)$</p>
<p>I chose the approach $f(t) = e^{\lambda t}$ and hence arrive for the first case at</p>
<p>$\lambda^2 e^{\lambda t} = e^{\lambda t}(3\lambda - 1) \rightarrow \lambda... | https://math.stackexchange.com/questions/563820/simple-differential-equations |
Question: <p>$$\frac{dx}{dy} = \frac{x(\alpha - \beta y)}{y(\delta x - \gamma)}$$ </p>
<p>How do I extract two differential equations (y as a function of x and x as a function of y) from the equation above? I could separate the variables, but I don't see how that would help.</p>
Answer: <p>I am certain (having recog... | https://math.stackexchange.com/questions/1115136/extracting-differential-equations |
Question: <p>I have a question about a rule in my textbook related to differential equations.</p>
<p>If we are considering a differential equation of the form $y"+ay'+b= f(x)$ such that $f(x)=P(x)e^{rx}\cos kx$ with $\deg(P)\leq m$, it is written that in order to determine the particular solution, I should set $y(x)=x... | https://math.stackexchange.com/questions/309532/duplication-differential-equations |
Question: <p>Can someone provide me a good reference about approximation techniques in continous domain (not piecewise nor numerical methods) for differential equations?</p>
Answer: <p>There really would be different types of methods for this, particularly dependent on how and what your differential equation is and al... | https://math.stackexchange.com/questions/432144/approximation-of-differential-equations |
Question: <p>How would I solve these differential equations?</p>
<p>$$y'+2y^2=\frac{6}{x^2}$$</p>
<p>I tried finding integral product but couldn't find its integral. And also tried to trasform into homogen equation. </p>
<p>and the second one is: </p>
<p>$$xe^{2y}y'+e^{2y}=\frac{\ln x}{x}$$ </p>
<p>How can I start... | https://math.stackexchange.com/questions/239844/two-differential-equations |
Question: <p>Is there literature available on solving differential equations of the type
$$f(x,y(x),y(\kappa x),y'(x))=0,$$
where $\kappa$ is a given constant? I know about the book Introduction to the Theory and Application of Differential Equations with Deviating Arguments by L.E. El'sgol'ts and S.B. Norkin from the ... | https://math.stackexchange.com/questions/197569/differential-equations-with-deviating-argument |
Question: <p>Whilst my knowledge of differential equations is somewhat limited, I was under the impression that the following was a valid equation to be solved yet it is unrecognised by wolfram alpha and I have no clue how to solve it:
$$dy = a\times x \times dx + b\times y$$
Is such a differential equation that contai... | https://math.stackexchange.com/questions/1455876/solving-strange-differential-equations |
Question: <p>I'm looking for an easy to read undergraduate book on partial differential equations, ideally something that is not much harder than a multivariable calculus/ordinary differential equations book.</p>
<p>I am preparing for a course which is using the text by Walter Strauss, but I found this text a bit diffi... | https://math.stackexchange.com/questions/4027697/easy-to-read-partial-differential-equations-book |
Question: <p>Today my professor told me that there are some differential equations that cannot be solved. Is this true? If it is true, why can they not be solved? How complex would that kind of differential equation have to be?</p>
Answer: <p><strong><em>Ordinary Differential Equations</em></strong> generally admit so... | https://math.stackexchange.com/questions/2337380/impossible-kinds-of-differential-equations |
Question: <p>I'm reading Fundamentals of Differential Equations by Nagle.
Given the equation
$$\frac{dy}{dx}=f(x,y)$$
Nagle says at times we can rewrite as an exact differential form
$$M(x,y)dx+N(x,y)dy=0$$
So it seems this is the case if it holds that
$$f(x,y)= \frac{-M(x,y)}{N(x,y)}$$
and if we do cross multiplying, ... | https://math.stackexchange.com/questions/2791046/relating-differential-equations-and-exact-differential-forms |
Question: <p>A book I'm using to teach myself differential equations claims the following:</p>
<p>If $y_{1}$ and $y_{2}$ are solutions to the differential equation $y' - a(t)y = q(t)$, then $y = y_{1} - y_{2}$ will be a null solution by linearity.</p>
<p>I understand there exists some linear combination of $y_{1}$ an... | https://math.stackexchange.com/questions/2006710/differential-equations-null-solutions |
Question: <ol>
<li>While solving differential equations, is it okay to find an expression containing <span class="math-container">$y$</span> and <span class="math-container">$x$</span> (without <span class="math-container">$y'$</span>) from which it's rather difficult to express <span class="math-container">$y$</span>,... | https://math.stackexchange.com/questions/3509715/about-differential-equations |
Question: <p>Can you help me solve this system of differential equations</p>
<p>$ x'= 4x - 2y $</p>
<p>$ y'= 3x - y - 2e^{3t} $</p>
<p>Initial conditions are $ x(0) = y(0) = 0 $</p>
Answer: <p>$\mathbf x' + \begin{bmatrix} -4&2\\-3&1\end{bmatrix} \mathbf x = \begin{bmatrix}0\\-2e^{3t}\end{bmatrix}$</p>
<p... | https://math.stackexchange.com/questions/1993377/system-of-differential-equations |
Question: <p>Is $x+y+2=0$ a differential equation without derivatives of order $n$, $n>0$? Could it be called a differential equation (for unknown $y(x)$) of order $0$? </p>
<p>If not, can we define differential equations of order zero?</p>
Answer: <p>You <em>could</em> call such equations "zero-order differential... | https://math.stackexchange.com/questions/1124912/ordinary-differential-equations-of-order-zero |
Question: <p>How to get <span class="math-container">$x(t),y(t)$</span> solutions for "product differential equations" (dotted on <span class="math-container">$t$</span>):</p>
<p><span class="math-container">$$\dot x \dot y= xy,\; \dot y^2-\dot x ^2= 1;$$</span></p>
<p>we have by solving quadratics</p>
<p><s... | https://math.stackexchange.com/questions/3741720/multiplied-differential-equations |
Question: <p>Solution curves for the differential equations
1) y' = max{y,y^2}
2) y‘ = min {y,y^2}</p>
<p>Please can anybody help me because I am really confused</p>
Answer: <p>Hints: On which region is $y > y^2$? On which region is $y < y^2$? Do you know what the solutions of $y' = y$ and $y' = y^2$ are?</p>... | https://math.stackexchange.com/questions/933301/problem-in-differential-equations |
Question: <p>As far as I know, the concept of stiffness is hard to define rigorously, but there are plenty of handwavy descriptions and motivating examples in the literature when it comes to <strong><em>linear</strong> differential equations</em>.
At the same time I have never seen an explicit and straightforward defi... | https://math.stackexchange.com/questions/1584388/stiff-nonlinear-differential-equations |
Question: <p>Equations (1) : $xy'+(1-x)y=1$ let $z=xy+1$</p>
<p>determine and solve the differential equation (2) whose general solution is the function $z$
.</p>
<p>-determine the general solution of (1)</p>
Answer: <p>If $z=xy+1$ then
\begin{eqnarray}
\frac{dz}{dx} &=& \frac{d}{dx}\left(xy+1\right) \\
... | https://math.stackexchange.com/questions/1244729/differential-equations-in-function |
Question: <p>I have just started a course on differential equations, and unfortunetely enough for me, we immediately used notation foreign for me, for example:</p>
<p>$$ x^2 \left(\dfrac{d^2y}{dx^2}\right)^2 = \sin( x)\;\textrm{ and}\;\; y \times \dfrac{d^2 y}{dx^2} = \sin(x)$$ were used as examples of non-linear ordi... | https://math.stackexchange.com/questions/310481/notation-of-differential-equations |
Question: <p><strong>Background:</strong> I need some help to understand the concept behind measure-driven differential equations. The solution of an ordinary differential equation is continuous. In order to describe discontinuous trajectories we use the concept of <em>distributions</em> (very well described in the boo... | https://math.stackexchange.com/questions/187327/measure-driven-differential-equations |
Question: <p>I know how to solve linear homogeneous ordinary differential equations with constant coefficients using the differential operator D, by using <a href="http://math.ucsd.edu/~dmeyer/teaching/20Dspring07/diffop2.pdf" rel="nofollow">this</a> method.</p>
<p>Is it possible to use a similar method (using the dif... | https://math.stackexchange.com/questions/23425/solving-ordinary-differential-equations-using-the-differential-operator-d |
Question: <p>I know what differential equations (DEs) are, but what exactly are partial differential equations (PDEs)?</p>
<p>I know the <a href="https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" rel="nofollow noreferrer"><em>Schrödinger equation</em></a> is a PDE.</p>
<p>I'm also looking for an intuitive unde... | https://math.stackexchange.com/questions/209691/what-exactly-are-partial-differential-equations |
Question: <p>What is the Implicit answer for this differential equation? </p>
<p>$\frac{dy}{dx} = y^{2}-4$</p>
<p>Help me i'm a newbie in differential equations.</p>
Answer: <p>Here is how you solve equations like yours. You are trying to solve $\frac{dy}{dx}=f(y)$. Rewrite it as $\frac{dy}{f(y)}=dx$, integrate on b... | https://math.stackexchange.com/questions/2126685/i-need-help-with-differential-equations |
Question: <p>I have a bit of a general question in regards to differential equations. Right now I'm working my way through "Differential Equations with Applications and Historical Notes (1972 edition)" by Simmons. There was a question regarding verifying that the orthogonal trajectories of the family of curves dictated... | https://math.stackexchange.com/questions/2328125/question-regarding-finding-differential-equations |
Question: <p>Hey right now I'm practising Fourierseries and found this problem, just so you know it's my first time using Fourier to solve differential equations.
$$ f''(x) + f(x) = 3\cos(2x) $$</p>
Answer: <p>$$
F[f''(x)+f(x)]=F[3\cos(2x)]
$$</p>
<p>or</p>
<p>$$
((i \omega)^2+1)F(\omega) = 3 \sqrt{\frac{\pi }{2}} \... | https://math.stackexchange.com/questions/2788663/fourier-and-differential-equations |
Question: <p>I have a nonlinear differential equation of the kind:</p>
<p>$ f(\ddot{x},\dot{x},x) =0$</p>
<p>I would like to know if there is <em>always</em> a way to write such a differential equation in a form like:</p>
<p>$ \dot{y} = g(y) $</p>
<p>that is to put the equation in the form of a set of first order d... | https://math.stackexchange.com/questions/2039621/how-to-reduce-second-order-nonlinear-differential-equations-into-sets-of-first-o |
Question: <p>I have two problem collections I am currently working through, the "Berkeley Problems in Mathematics" book, and the first of the three volumes of Putnam problems compiled by the MAA. These both contain many problems on basic differential equations.</p>
<p>Unfortunately, I never had a course in differentia... | https://math.stackexchange.com/questions/90006/differential-equations-reference-for-putnam-preparation |
Question: <p>Currently I'm taking the Differential Equations course at college, however the problem is the book used. I'll try to make my point clear, but sorry if this question is silly or anything like that: the textbook used (William Boyce's book) seems to assume that the reader doesn't familiarity with abstract mat... | https://math.stackexchange.com/questions/400806/differential-equations-reference-request |
Question: <p>Is the ordinary differential equations course a prerequisite for the partial differential equations course for a person who has passed the integral calculus course?<br/>
Is it really required to have passed an ordinary differential equations course to be able to learn Fourier Theory?<br/>
What is the prere... | https://math.stackexchange.com/questions/1076091/partial-differential-equations-course-and-differential-geometry-prerequisites |
Question: <p>Can you help me please to solve this system of differential equations</p>
<p>[ \begin{cases}
\dot{x_{1}}=2x_{1}-x_{2}\\
\dot{x_{2}}=4x_{1}-2x_{2}-2t^{-3}
\end{cases}
]</p>
<p>thanks :) </p>
Answer: <p><strong>HINT</strong> </p>
<p>Extract $x_2$ from the first equation and plug into the second. This w... | https://math.stackexchange.com/questions/655744/system-of-differential-equations |
Question: <p>I have a system of two Second Order differential equations
$$
r^2 \ddot{r} - r^3(\dot{\varphi}^2 +\omega^2) =-GM
$$
$$
r \ddot{\varphi} + 2\dot{r}(\dot{\varphi}+\omega)=0
$$
which I am supposed to decouple using the conservation size $ (\dot{\varphi}+\omega)r^2 $ I have shown, that it is indeed a conservat... | https://math.stackexchange.com/questions/2570271/decouple-differential-equations |
Question: <p>Usually for second order differential equations, we get a general solution with 2 constants that are obtained by using the boundary conditions. What about for a coupled pair of second order differential equations? Would I be right to think that the same applies? </p>
Answer: <p>You will have $4$ constants... | https://math.stackexchange.com/questions/126986/freedom-of-second-order-differential-equations |
Question: <p>Can you help me to find all solutions of differential equation $y'^2-(x+y)y'+xy=0$?</p>
<p>I wrote this equation as product of explicit equations:</p>
<p>$$(y'-x)(y'-y)=0$$</p>
<p>Then I found zeroes: $y'-x=0 \Longrightarrow y'=x \Longrightarrow y=\frac{x^2}2+C_1$</p>
<p>$y'... | https://math.stackexchange.com/questions/89727/explicit-differential-equations |
Question: <p>I am putting together a list of types of first and second order differential equations and I am struggling with the definition of homogeneous and nonhomogeneous. Can anyone clarify the definitions for me please? </p>
Answer: <p>The word <em>homogeneous</em>, somewhat confusingly, is used in two different... | https://math.stackexchange.com/questions/3215032/defining-homogeneous-differential-equations |
Question: <p>Folks,</p>
<p>In differential equations there are two things:
1. Modeling (form differential equation based on physical system or real life problem)
2. Solving differential equation
Need help for first part.</p>
<p>Could you please provide link to problem sets or practice set of Modeling Differential Eq... | https://math.stackexchange.com/questions/3035396/required-practice-problems-of-modelling-differential-equations |
Question: <p>I am looking for an advanced book on partial differential equations that makes use of functional analysis as much as possible. All the books I have looked in so far either shy away from functional analysis and try to avoid even basic concepts, or present results from functional analysis I know anyway just ... | https://math.stackexchange.com/questions/1989007/advanced-book-on-partial-differential-equations |
Question: <p>After posting this <a href="https://math.stackexchange.com/questions/4521706/suggestion-of-around-6-books-in-the-topics-abstract-algebra-linear-algebra">question</a>, I have decided to separate the contents into multiple questions.</p>
<p>Reasons I am doing this:</p>
<ul>
<li><p>Right tag for each topic, s... | https://math.stackexchange.com/questions/4523091/differential-equations-book-for-self-learning |
Question: <p>I have two questions regarding solving differential equations given initial conditions:</p>
<p>1) When do you substitute the initial conditions into the equation to calculate the value of the constant "<span class="math-container">$c$</span>". Do you substitute it once you integrate both sides of the diff... | https://math.stackexchange.com/questions/2951485/solving-differential-equations-c-value |
Question: <p>Given these differential equations:</p>
<p>$\frac{d^2x}{dt^2} = 2\Omega\frac{dy}{dt}\sin(\lambda) - \frac{g}{L}x$</p>
<p>$\frac{d^2y}{dt^2} = -2\Omega\frac{dx}{dt}\sin(\lambda) - \frac{g}{L}y$ </p>
<p>Now making the following substitutions:</p>
<p>$\frac{dx}{dt} = u$ and $\frac{dy}{dt} = v$ we have the... | https://math.stackexchange.com/questions/325545/differential-equations-notations-confusion |
Question: <p>I have found the following example in one of my courses but I don't have any similar exercises resolved so I would like to know how to solve this:</p>
<p>The differential equations system is the following:</p>
<p>$$x_1' = 3x_1 - 2x_2 + e^t$$
$$x_2' = 2x_1 - x_2 + 2e^{2t}$$</p>
<p>a) Write the system in ... | https://math.stackexchange.com/questions/1778640/differential-equations-system |
Question: <p>Consider the following system of differential equations:
\begin{align}
x_1'=f_1(x_1,x_2)\\
x_2'=f_2(x_1,x_2)
\end{align}
Assume that a solution $x(t)$ exists for $t\in (-T,T)$. Let $g:\mathbb{R}^2\to\mathbb{R}$ be a smooth function. Now we consider the following system of differential equations:
\begin{ali... | https://math.stackexchange.com/questions/1483787/convolution-and-differential-equations |
Question: <p>How may I solve this differential equations:</p>
<p>$$y''+4y=12x^2-16x\cos(2x)?$$</p>
Answer: <p>Hint: Solve the homogeneous part first: the part $y''+4y=0$ by letting $y=e^{\lambda x}$. Then differentiate, substitute, simplify and solve.</p>
<p>Then solve the rest using method of undetermined coefficie... | https://math.stackexchange.com/questions/1369886/differential-equations-of-second-order |
Question: <p>Can someone please explain how associated homogeneous linear differential equations work with an example?</p>
Answer: <p>Lets say you have the linear differential equation
$y'' + y =3x$;</p>
<p>The associated homogeneous equation is
$y'' + y = 0$</p>
<p>The set of the solutions to the homogeneous equat... | https://math.stackexchange.com/questions/1971539/associated-homogeneous-linear-differential-equations |
Question: <p>So I have been working with these differential equations that are dependent on each other:
<span class="math-container">$$
\begin{aligned}
\frac{dy}{dt} &= 0.1y-0.01(10000-a)\\
\frac{da}{dt} &= 0.1a-10y
\end{aligned}
$$</span>
So the first equation represents the change rate of predatory fish while... | https://math.stackexchange.com/questions/3614288/dependent-differential-equations |
Question: <p>An initial amount <span class="math-container">$\alpha$</span> of a tracer (such as a dye or a radioactive isotope) is injected into Compartment 1 of the two-compartment system shown in the Figure. At time <span class="math-container">$t > 0$</span>, let <span class="math-container">$x_1 (t)$</span> and... | https://math.stackexchange.com/questions/4681746/differential-equations-applications |
Question: <p>Exact differential equations come from finding the total differential from some multivariable function.</p>
<p>In the exact differential equation $M\mathrm{d}x+N\mathrm{d}y=0$</p>
<p>M and N are considered to be partial derivatives of some potential function... So why aren't exact differential equations ... | https://math.stackexchange.com/questions/929973/why-arent-exact-differential-equations-considered-pde |
Question: <p>Is there a way to define differential equations on a scheme? If so, is there a Galois-like theory for adding solutions to the differential equation to the sections of the Scheme?</p>
Answer: <p><strong>Question:</strong> "If so, is there a Galois-like theory for adding solutions to the differential e... | https://math.stackexchange.com/questions/4171145/solving-differential-equations-on-a-scheme |
Question: <p>Hi: I am researching about relationships between Differential Geometry and Differential Equations. I am looking for <strong>examples and references of the use of geometric concepts to solve or analyze differential equations</strong>.</p>
<p>For example, in <em>Differential Equations With Applications and H... | https://math.stackexchange.com/questions/4409559/geometrical-insights-on-differential-equations |
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