For all real values of \( x \) and \( y \), the partial differential equation in terms of \( \psi(x, y) \) given by
\[
\frac{\partial^2 \psi}{\partial x^2} + 2 \frac{\partial^2 \psi}{\partial x \partial y} - 3 \frac{\partial^2 \psi}{\partial y^2} = 0
\]
is ________