$\frac{dy}{dx} = e^{x-y} + x^2e^{-y} = \frac{e^x + x^2}{e^y}$.
As the $x-$terms and $y-$ terms have been separated, we can integrate them with $dx$ and $dy$ respectively.
$e^ydy = (e^x + x^2)dx$
$e^y = e^x + \frac{x^3}{3} + c$
a is the correct answer.