Textbook Problem

Let L be a nonzero real number.

(a) Show that the boundary-value problem y" + λy = 0, y(0) = 0, y(L) = 0 has only the trivial solution y = 0 for the cases λ = C and λ < 0.

(b) For the case λ > 0, find the values of λ for which this problem has a nontrivial solution and give the corresponding solution.