Recall that the general solution to the following boundary value problem for the heat equation ut = Uxx u(0, t) = To, u ( L, t ) = TL u (x, 0) = 4(2) is of the form u(ac, t) = v(x, t) + > bre( "T )'t sin(nn ac n=1 for v(x, t) = To+ (TL - To) F, and for bn's being the Fourier sine series of (x) - v(x, 0). Let L = T. a. Solve the boundary value problem when p(x) = x. To = TT = 2