2. (a) Prove that the function u(x, t) = sin(7x) cos(4nt) is the solution of the wave equation with the specified initial-boundary conditions. Utt = 16uzx, I E (0,1) u(0, 0) = sin(T2), [0, 1] ut(1,0) = 0, X [0, 1] u(0, t) = 0, te [0,1] u(1,t) = 0, te [0,1] (b). Solve the initial-boundary value problems in (a) by the finite differ- ence method with h = 0.05, At = h/c. Use Matlab's mesh command to plot the solution