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Does there exist a twice differentiable periodic function $f$ such that $f''(x) + f(x) =\sin(x)$ for all $x \in [-\pi, \pi]$?

How to solve this differential equation using Fourier series? I know only basics of Fourier analysis. I don`t know any inversion formula for Fourier series.

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    I guess it is more appropriate to use the Laplace Transform here, rather than Fourier's.2012-04-17

3 Answers 3