A PDE I can't solve by seperation of variables

[NapoleonZ]

Homework Statement

Homework Equations

After simplification, the PDE is

(b^2/a^2)(d^2 v/ d x^2) + (d^2 v/ d y^2) = -1

The Attempt at a Solution

Obviously, it can't be solved by separation of variables. And I also failed in similarity solution.

 

[quZz]

Are a and b constants? If so, you need to change the x-scale: x = x' * b/a and get the standard Poisson's equation.

 

[NapoleonZ]

Are a and b constants? If so, you need to change the x-scale: x = x' * b/a and get the standard Poisson's equation.

Yes, they are.