(10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, with initial condition and with boundary conditions au(t, x) = 38u(t, x), te [0, ∞), [0,3]; 2, x = 0, u(0, x) = f(x)= 3 TE Find the solution u using the expansion u(t, 0) = 0, zu(t, 3) = 0. u(t, x) = vn(t) wn(x), n=1 with the normalization conditions 3 in (2n²=− 1) ) = 1. a. (3/10) Find the functions wn, with index n > 1. Wn b. (3/10) Find the functions vn, with index n > 1. Un c. (4/10) Find the coefficients C, with index n > 1. Un (0) 1, wn = Cn =