Find a non-trivial solution in the first quadrant for:

$\displaystyle f+\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y}=\int_{x}^{\infty}\int_{y}^{\infty} f(u,v)dvdu$

Hint: Can you think of a trial function of two parameters $\displaystyle f(x,y;a,b)$ that would make the right side converge?