2. (30 points) In your answers for this problem, you may use n to represent an arbitrary positive integer. a) Find all the values of A so that the differential equation u" + Au = 0 has a solution (other than u = 0) with boundary conditions u(0) = u(2) = 0. b) Find all the solutions of the partial differential equation 25 dy dzy aT2 at2 of the form y(x, t) = u(x)v(t) with boundary conditions u(0) = u(2) = 0 and initial condition du (0) = 0