Given the following boundary value-nitial value problem for the heat equation on [0, 1] : 1 02 u at = 9 272 u(0, t) = 0, u( 1, t) = 0, u(x, 0) = 7 sin 3mr. (a) If u(x, t) is the solution to this problem, find an initial boundary value problem satisfied by w(x, t) = estu(x, t). (b) Solve the problem found in part (a) for w(I, t). (c) Find the solution u(x, t) to the original problem. (d) Find the time 71 such that u(x, t) Ti