GATE EC 2022 Set 1 Q15 — Differential Equations

Consider the following partial differential equation $\text{(PDE)}$

$$a \frac{ \partial^{2} f(x ,y)}{\partial x^{2}} + b \frac{ \partial^{2} f(x ,y)}{\partial y^{2}} = f(x, y),$$

where $a$ and $b$ are distinct positive real numbers. Select the combination(s) of values of the real parameters $\xi$ and $\eta$ such that $f(x, y) = e^{(\xi x + \eta y)}$ is a solution of the given $\text{PDE}.$