GATE Electronics and Communications (EC) 2022 Solved Paper

Consider the following partial differential equation (PDE)
$\mathit{a}\frac{{\partial }^2\mathit{f}\left(\mathit{x},\mathit{y}\right)}{\partial {\mathit{x}}^2}+\mathit{b}\frac{{\partial }^2\mathit{f}\left(\mathit{x},\mathit{y}\right)}{\partial {\mathit{y}}^2}=\mathit{f}\left(\mathit{x},\mathit{y}\right)$
where a and b are distinct positive real numbers. Select the combination(s) of values of the real parameters 𝜉 and 𝜂 such that f(x, y) = e(ξx + ny) is a solution of the given PDF.