Suppose we have this differential equation $\frac{d^{2}F}{dx^2}+\frac{d^{2}F}{dy^{2}} = 1$ with some boundary conditions
This equations looks like the wave equation with $c=i$ except from the inhomogenous part.Can I solve the wave equation with $c=i$ with some boundary conditions then find the solution of $\frac{d^{2}F}{dx^2}+\frac{d^{2}F}{dy^{2}} = 1$ by setting all the initial conditions to 0?