Consider vt = c2uxx – v (0 < x < L, t > 0), v(0, t) = 0, v(L, t) = 0, v(x, 0) = f(x), where the term – v models heat transfer to the surrounding medium kept at temperature 0. Reduce this PDE by setting v(x, t) = u(x, t) w(t) with w such that u is given by (9), (10).