I know how to solve this homogeneous problem using separation of variables . Here, $u$ is from $\mathbb{R}^2 \rightarrow \mathbb{R}$ $$u_{xx}+u_{yy} = 0$$
But, How to solve this non homogeneous equation using separation of variables $$ u_ {xx} + u_{yy} = 1 $$ There are no boundary conditions given in question.
I am new in solving PDE, so please explain the answer as well.