🚀 go-pugleaf

Not familiar with elliptic partial differential equation...wondered if 
there is code for solving eignevalue/eigenfunction of elliptic PDE. 

P[\phi(x,y)]=E \phi(x,y)   in the region 0<x<x0, and 0<y<y0. E is eignevalue 
with eigenfuction \phi(x,y). P differential operator defined by 

P=(\partial_{x,x} + \partial_{y,y})+ a*(x* \partial_{y} -y* \partial_{x})+
  b*(x**2+y**2)

where a, b are constant
with boundary condition \phi(x,y)=0 for x=0, x=x0, y=0, and y=y0.

Ideally, I am looking for exact solution. However, I am no longer optimistic 
there is exact solution. I also realize NAG lib(mark 13 version) has a general 
routine for solving elliptic PDE, but it does not solve the
eigenvalue/eigenfuntion problem...
Any help or suggestion...