Eigenvalue problem:
$y''+ \lambda y = 0$ subject to $y'(0) = 0$ and $y(1) + y'(1) = 0$
The question is:
show that the eigenvalues are given by $\lambda = \mu^2$ with $\mu$ any root of $ \mu \tan \mu$
I actually have some solution which says that for $\lambda =\mu^2 >0$ we find solutions $y= A\cos\mu x + B\sin \mu x$.
I can continue the problem by substituting the boundary conditions into the the solution equation....
Can anyone enlighten me with how they got to the answer?