Consider the eigenvalue problem on [0,T] Luu"-4u' = = Xu with boundary conditions u(0) = u(π) = 0. (a) [6 points] Find its eigenvalues and eigenfunctions. Note that eigenfunctions should not be identically zero. (b) [6 points] Find an μ(x) > 0 such that := p(x)C is self-adjoint on X = {y Є C² [0, 1]: y(0) = y(T) = 0}. Then show that any pair of distinct eigenfunctions found in part (a) are orthogonal under the weighted L²-norm on [0,7] with the weight μ(x).