Consider the following problems:

(a) State the differential equation for the Sturm-Liouville problem where \(r(x)=\) \(x, p(x)=x^{-1}\), and \(q(x)=0\).

(b) Using the transformation \(x=e^{t}\), show that this differential equation reduces to \(\frac{d^{2} y}{d t^{2}}+\lambda y=0\).

(c) Given the boundary conditions \(y(1)=0\) and \(y(e)=0\) for the differential equation in (a), what are the corresponding eigenvalues and eigenfunctions?