(a) Find the eigenvalues and eigenfunctions of the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) 20 = Yn(x) = x²y". - '+xy' + yo, y(1) = 0, y(8) = 0 n = 1, 2, 3, ... n = 1, 2, 3,... (b) Put the differential equation in self-adjoint form. dx C (c) Give an orthogonality relation. For m = n, 81 ] ) y = 0 xXxXxXxXx dx = 0.