Answer
$e^y-x^3=c$
Work Step by Step
As we are given that $\dfrac{dy}{dx}=3x^2 e^{-y}$
Re-arrange the given equation as follows:
$\dfrac{dy}{dx}=\dfrac{(3x^2)}{e^y}$
This implies that $(e^y) dy=(3x^2) dx$
Now take the help of integration.
Then $\int (e^y) dy=\int (3x^2) dx$
Use formula: $\int x^n dx=\dfrac{x^{n+1}}{n+1}+c$
$\int (e^y) dy=\int (3x^2) dx \implies e^y=\dfrac{3x^{2+1}}{2+1}+c$
Hence, $\dfrac{3x^{3}}{3}+c =e^y\implies e^y-x^3=c$
