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so now what we want to do is we want to
sum up many of these solutions using the
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sum up many of these solutions using the
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sum up many of these solutions using the
superposition principle so if I go back
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superposition principle so if I go back
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superposition principle so if I go back
now
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now
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now
i'm going to write the original
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i'm going to write the original
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i'm going to write the original
differential equation
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so i'm just going to go back and just
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so i'm just going to go back and just
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so i'm just going to go back and just
rewrite this
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rewrite this
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rewrite this
and i'm going to write the right-hand
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and i'm going to write the right-hand
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and i'm going to write the right-hand
side using its fourier series 1 over n
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side using its fourier series 1 over n
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side using its fourier series 1 over n
sine NT
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sine NT
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sine NT
where n is odd
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where n is odd
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where n is odd
ok and this is the problem we originally
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ok and this is the problem we originally
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ok and this is the problem we originally
wanted to solve and essentially what