The solution of the differential equation $y d x+\left(x+x^2 y\right) d y=0$, is

$-\frac{1}{x y}+\log y=C$

We have,

$y d x+\left(x+x^2 y\right) d y=0$

$\Rightarrow y d x+x d y+x^2 y d y=0$

$\Rightarrow \frac{d(x y)}{(x y)^2}+\frac{1}{y} d y=0$          [Dividing throughout by $(x y)^2$]

On integrating, we get $-\frac{1}{x y}+\log y=C$