I have been given the problem:
$$ \begin{cases} u_{xx}+u_{yy}=y(1-y)(3\sin x - \sin3x) & 0<x<\pi,0<y<1 & \\ u(x,0)=0 & 0<x<\pi & (1) \\ u(x,1)=0 & 0<x<\pi & (2) \\ u(0,y)=u(\pi,y)=0 & 0<y<1 & (3) \end{cases} $$
I have not solved any problem with this type of condition. Every problem I have seen has the condition (1) along with a condition $u_t(x,0)=g(x)$ (Initial value problem), combined with (3) (A certain type of boundary conditions). I don't know how to proceed. Is separation of variables the only way?