Question

Solve the following differential equation:
$\frac{dy}{dx}=e^{x-y}+x^2{e}^{-y}$

Answer 1

$\Rightarrow \frac{dy}{dx}=e^{-y}(e^x+x^2)$

$\Rightarrow e^{y}dy=(x^2+e^x)dx$

Integrate on both sides

$\Rightarrow e^y=e^x+\frac{x^3}{3}+C$, where $C$ is a constant