Chapter 10.2, Problem 9E

In Problems 9-14, find the values of $\lambda$ (eigenvalues) for which the given problem has a nontrivial solution. Also determine the corresponding nontrivial solutions (eigenfunctions).

$y^{″}+\lambda y=0$; $0<x<\pi$,

$y\left(0\right)=0$, $y^{\prime }\left(\pi \right)=0$