Solve the PDE ut = k(uxx +2 u) , 0 0 subject to the following boundary conditions using the method of separation of variables. Note that A, k and are fixed positive constants. ux(0, t) = 0 , ux(L, t) = 0 , u(x, 0) = f (x) = A + 2 cos( x L ) + 3 cos( 4 x L )