Use the eigenfunction expansion to solve the non-homogeneous PDE: 0 0 Utt = kurz + tem, u(t,0) = 0, ult, L) = 0, u(0,x) = x, Ut(0, x) = 0, Assume k > 0. Note that the eigenfunctions for the non-homogeneous version of the PDE are given by On = sin( *x), for n > 0, where n e N. Write your solution u(t, x). Use the eigenfunction expansion to solve the non-homogeneous PDE: 0 0 Utt = kurz + tem, u(t,0) = 0, ult, L) = 0, u(0,x) = x, Ut(0, x) = 0, Assume k > 0. Note that the eigenfunctions for the non-homogeneous version of the PDE are given by On = sin( *x), for n > 0, where n e N. Write your solution u(t, x)