I am trying to solve the following BVP:
$-\Delta u + b\cdot \nabla u + u = k$
On the unit square in $\mathbb{R}^2$ with homogenous Dirichlet boundary conditions where $b$ is a constant vector field, and $k$ is a positive constant.
I would at least like a push in the right direction here if not a detailed explanation. I tried separation of variables-that didn't work. Is there a closed-form Green's function? Is there just a way to intuitively solve it by inspection?