$\text{ Solve }\frac{dy}{dx}=x^3{y}^3-xy$

$\begin{array}{l}\text{ G.E }\frac{dy}{dx}+xy=x^3{y}^3\Rightarrow \frac{1}{y^3}\frac{dy}{dx}+\frac{x}{y^2}=x^3\\ \text{ Put }\frac{1}{y^2}=z\Rightarrow \frac{dz}{dx}-2xz=-2x^3;I.F=e^{-x^2}\\ \text{ General solution }z{e}^{-x^2}\int -2x^3{e}^{-x^2}dx\\ \text{ Put }{x}^2=t\Rightarrow z{e}^{-x^2}=-\int t{e}^{-t}dt\\ \\ \Rightarrow \frac{1}{y^2}{e}^{-x^2}=x^2{e}^{-x^2}+e^{-x^2}+c\\ \Rightarrow \left(x^2+1+c{e}^{x^2}\right)y^2=1\end{array}$