Question

Get a differential equation from $x^y=e^{x-y}$.

Answer 1

$x^y=e^{x-y}$

$y\log x=x-y$

Diff on both sides

$\frac{y}{x}+\log x\frac{dy}{dx}=1-\frac{dy}{dx}$

$(1+\log x)\frac{dy}{dx}=\frac{x-y}{x}$