PROBLEM 2: Eigenvalues and Eigenfunctions In the separation of variables solution of a partial differential equation, the solution of the differential equation q"(x) + Ap(x) = 0 with boundary conditions yields the eigenvalue-eigenfunction pairs An, On. Determine the eigenvalues and eigenfunctions for these sets of boundary conditions, and by integration, show that the eigenfunctions are orthogonal. a q'(0) = 0, Q(L) = 0 [10 pts] b Q'(0) = 0, q'(L) =0 [10 pts]