Proceed as in this example and find an explicit solution of the given initial$-$value problem.

$,\frac{dy}{dx}=y^{2}sin(x^2),y(-3)=\frac{1}{9}$

$[9-{\displaystyle \underset{-3}{\overset{x}{}}}sin(t^2)dt{]}^{-1}$

$[81-{\displaystyle \underset{-3}{\overset{x}{}}}sin(t^2)dt{]}^{-1}$

$[\frac{1}{81}-{\displaystyle \underset{-3}{\overset{x}{}}}sin(t^2)dt{]}^{-1}$

$\frac{1}{9}-{\displaystyle \underset{-3}{\overset{x}{}}}sin(t^2)dt$

$81-{\displaystyle \underset{-3}{\overset{x}{}}}sin(t^2)dt$