10. (a) In Exercise 2.2.6, we found the general solution of Utt = Uzz - u(0,t) = u(1,t) = 0, u(x, 0) = f(x), u₁(x, 0) = g(x), 0<x<1, t> 0, t> 0, 0 < x < 1, 0 < x <1. Find the coefficients in the general solution. (b) Suppose f(x) = -100x3 (1-x)(x-0.75), and g(x) = 1-x. Using the first 10 terms in the series, plot the solution surface and enough time snapshots to display the dynamics of the solution. (c) What happens to the solution as too? Explain your answer in light of (a) and the physical interpretation of the problem. Does (b) reflect this?