2. Consider the nonhomogeneous wave problem Utt = Uxx - 2e " for 0 0, u(0, t) = 0, u(1, t) = 0 for t > 0, (2) u(x, 0) = -(e-3x -1), ut(x,0) =0 for 0 0, subject to the homogeneous boundary conditions v(0, t) = v(1, t) = 0 for t > 0. (b) Using the method of separation of variables, solve the initial boundary value prob- lem for v. [Hint. Find v(x, 0) and vt(x, 0).] (c) Hence, solve the non-homogeneous problem (2)