Answer
$2 \sqrt y -\dfrac{x^3}{3} =C$
Work Step by Step
As we are given that $\dfrac{dy}{dx}=x^2 \sqrt y$
and, $\dfrac{dy}{(\sqrt y)}=x^2 dx$
Need to integrate the above expression, that is, $\dfrac{dy}{(\sqrt y)}=x^2 dx$, to get .
$\int \dfrac{dy}{\sqrt y}= \int x^2 dx$
or, $2 (\int \dfrac{dy}{2\sqrt y})= \int x^2 dx$
$\implies (2 \sqrt y)=\dfrac{x^3}{3}+C$
Thus, $2 \sqrt y -\dfrac{x^3}{3} =C$
