I will assume that U1 and U2 are constants. First you need to move them to zero. So let and let which gives thus

The problem now changes

subject to

If there was no source term then a separation of variables would lead to

but because of the source term we try

sub. into the PDE and group terms accordiong to . You should get an ODE for which you can solve. Remember, you'll need a sine series for the