I think it would benefit everyone if you wrote down the entire system of equations and let everyone know what are the independent and dependent variables. For example is $\rho$ constant or a function of ???. I'm guessing you have 3 unknowns, $\rho$, $u$ and $v$. You have a stream function which I'm guessing came from a continuity equation? and I'm sure there's another equation floating around (again, you have 3 unknown's).

I think by giving more details on what you've done will help those wanting to help you.