The solution of the differential equation

$\left(x^2-y{x}^2\right)\frac{dy}{dx}+y^2+x{y}^2=0$, is

The given differential equation is

$\begin{array}{l}{x}^2(1-y)\frac{dy}{dx}+y^2(1+x)=0\\ \Rightarrow x^2(1-y)dy+y^2(1+x)dx=0\\ \Rightarrow \frac{1-y}{y^2}dy+\frac{1+x}{x^2}dx=0\end{array}$

On integrating, we get 

$-\frac{1}{y}-\log y-\frac{1}{x}+\log x=C\text{ or, }\log \left(\frac{x}{y}\right)=\frac{1}{x}+\frac{1}{y}+C$