So I'm trying to apply FDM (Finite Difference Method) on this problem but it seems line I'm missing some data as I know nothing about the second member g(x,y). Hence, even if I transform the problem into the matrix form, I won't be able to extract the solution u(x,y) without knowing what g(x,y).

I saw online some people putting a function that respects the boundary conditions, and then find what g(x,y) but I can't get the process.