Questions on "Partial Differential Equations", as opposed to "ordinary differential equations".

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Using a multivariate chain rule to solve a partial differential equation

(a) Let $a$ and $b$ be some parameters for which $a^2 + b^2$ > 0 and use the substitution $u = bx−ay$ and $v = ax+by$, to rewrite the partial differential equation $af_{x} + bf_{y} = 0$, into a ...