Use separation of variables/Fourier method to solve(adsbygoogle = window.adsbygoogle || []).push({});

u_{t}- 4u_{xx}= 0, -pi<x<pi, t>0

u(-pi,t) = -u(pi,t), u_{x}(-pi,t) = -u_{x}(pi,t), t>0.

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What I got is that (n+1/2)^{2}are eigenvalues (n=0,1,2,3,...) and cos[(n+1/2)x)] is an eigenfunction.

Instead of two sets of eigenvalues, there is only one set. I cannot find another set of eigenvalues.

My question is: is sin[(n+1/2)x)] also an eigenfunction for this problem? Why or why not?

Thanks for any help!

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# Fourier method | eigenfunctions

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