Chapter 12, Problem 2RE

Use separation of variables to find product solutions of

$\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}+2\frac{\partial u}{\partial x}+2\frac{\partial u}{\partial y}=0$

Is it possible to choose a separation constant so that both X and Y are oscillatory functions?