Let L be a nonzero real number. (a) Show that the boundary-value problem y'' + y = 0, y(0) = 0, y(L) = 0 has

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 = 0 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.