Answer
$e^y-x^3=c$
Work Step by Step
Given: $\dfrac{dy}{dx}=3x^2 e^{-y}$
This can be re-written as:
$\dfrac{dy}{dx}=\dfrac{3x^2}{e^y}$ or, $e^y dy=3x^2 dx$
We need to integrate the above expression.
we have $\int e^y dy=\int 3x^2 dx$
We know that $\int x^n dx=\dfrac{x^{n+1}}{n+1}+c$
This implies that $e^y=\dfrac{3x^{2+1}}{2+1}+c$
Thus,
$e^y-x^3=c$
