Answer
$y=Ae^{\frac{x^3}{3}}$
Work Step by Step
We are given that $\dfrac{dy}{dx}=x^2y$
We will separate the variables to obtain:
$\dfrac{dy}{y}=x^2 dx$
Integrate to obtain:
$\int \dfrac{dy}{y}=\int x^2 dx$
This implies that $\ln |y|=\dfrac{x^3}{3}+C$
or, $e^{\ln |y|}=e^{\frac{x^3}{3}}+C$
Therefore, we have: $y=Ae^{\frac{x^3}{3}}$
