Consider the partial differential equation
$$ \Delta u = au - b,~~~~~ x \in \Omega \subset \mathbb{R}^{n},~a,b>0$$ $$ \frac{\partial u}{\partial n} = 0~~ \text{on}~ \partial \Omega.$$ Using some transformation, is there any way to convert it into the form $$ \Delta v = c,~~~~~ x \in \Omega \subset \mathbb{R}^{n}$$ with some appropriate boundary conditions. Because I know, how to handle Poisson's equation but don't know how to handle this equation, that is, how to derive solution to this PDE?