Question 3 Assuming heat diffuses along a 1D rod of length L and the following conditions apply du(x, t) azu(x, t) = K at 3x2 u(0, t) = 0 u(L, t) = 0 a. ) If the length of the rod is L = 2 and the initial condition takes the form: u(x, 0) = f (x) = nix M Bn Sin ) = 10 n = 1,2,3. n=1 Calculate the constant By and write the complete final solution. [1 mark] b.) Ifn = 1 substitute the final solution back into the diffusion equation and prove that it is indeed a valid solution. [1 mark]