differential equation

6. Use the eigenfunction expansion method to solve the following initial and boundary value problem: Ut = Uxx + 2xt + 2te * sin(2x), O 0, u(0, t) = 0, U( 7, t) = it. u(x, 0 - sin x. (Hint: First find a function r(x, t) that satisfies boundary conditions i.e. r(0, t) = 0 and r(7, t) = at2. Then consider v = u - r.)