Exercise 5.3 a)

I made a bit of mess of the formal solution in exercise 5.3 a) in the lecture today. In particular the solution of T_0'' = - \lambda_0 T_0 for t >=0, when \lambda_0 =0. As we speculated, the general solution of this ODE is indeed T_0(t) = \bar{a}_0 + \bar{b}_0 t for some constants \bar{a}_0 and \bar{b}_0 that are to be determined from the initial conditions of the PDE. See the solution suggestions for one way of solving this problem.