Given the Poisson's equation
$$-\nabla^2 u(x,y) = f(x,y) \in \Omega$$
$$u = u_0(x,y) \in \partial \Omega$$
with $$\Omega = [0,1]^2$$
I want to derive the analytical expression of $f(x,y)$ so that the exact solution is
$$u_0(x,y) = 10x + \tanh(10x-10)$$
Could you please give just a hint on how to do this?
I have only studied separation of variables for the heat equation during my course.