$\text{ The solution of the D.E }\left(2y+x{y}^3\right)dx+\left(x+x^2{y}^2\right)dy=0\text{ is }$

$\begin{array}{l}(2\mathrm{ydx}+\mathrm{xdy})+\left({\mathrm{xy}}^3\mathrm{dx}+{\mathrm{x}}^2{\mathrm{y}}^2\mathrm{dy}\right)=0\\ \text{ Multiplying by }\mathrm{x}\\ \left(2\mathrm{xydx}+{\mathrm{x}}^2\mathrm{dy}\right)+\left({\mathrm{x}}^2{\mathrm{y}}^3\mathrm{dx}+{\mathrm{x}}^3{\mathrm{y}}^2\mathrm{dy}\right)=0\end{array}$

$\left(2\mathrm{xy}+{\mathrm{x}}^2\frac{\mathrm{dy}}{\mathrm{dx}}\right)+\left({\mathrm{x}}^2{\mathrm{y}}^3+{\mathrm{x}}^3{\mathrm{y}}^2\frac{\mathrm{dy}}{\mathrm{dx}}\right)=0$

$\begin{array}{l}\to d\left(x^{2}y\right)+\frac{1}{3}d\left(x^3{y}^3\right)=0\\ \to \int d\left(x^{2}y\right)+\frac{1}{3}\int d\left(x^3{y}^3\right)=0\\ \to x^{2}y+\frac{x^3{y}^3}{3}=C\end{array}$