Find the eigenvalues and eigenfunctions of the given Sturm-Liouville problems: a. (y^{prime prime}+lambda y=0, y^{prime}(0)=0=y^{prime}(pi)). b. (left(x y^{prime} ight)^{prime}+frac{lambda}{x} y=0, y(1)=yleft(e^{2} ight)=0).

Find the eigenvalues and eigenfunctions of the given Sturm-Liouville problems:

a. \(y^{\prime \prime}+\lambda y=0, y^{\prime}(0)=0=y^{\prime}(\pi)\).

b. \(\left(x y^{\prime}\right)^{\prime}+\frac{\lambda}{x} y=0, y(1)=y\left(e^{2}\right)=0\).