- 1,270

- 0

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.

=============================

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!