List of top Partial Differential Equations Questions on Second Order Linear PDEs

Consider the following partial differential equation:
\[ a\frac{\partial^2 f(x,y)}{\partial x^2} + b\frac{\partial^2 f(x,y)}{\partial y^2} = 8f(x,y) \]
where \(a\) and \(b\) are distinct positive real numbers.
The combination(s) of the values of the real parameters \(\xi\) and \(\eta\) for which \(f(x,y) = e^{2\xi x+\eta y}\) is a solution of the given partial differential equation, is/are