(a) The function p(x, t) satisfies the partial differential equation a4 dt in 0 x 1 for t 0, with 0 < d < u, and satisfies the boundary and initial conditions (0, t) = (1,t) = 0, d +2d_0 dt dx -(x, 0) = 0. dt +20 ad dx Use separation of variables to find the most general form of p(x, t). (b) If [14 marks p(x,0) = e-2x sin 2x, find the solution when v = 2. Plot the graph of at x = as a function of t.