The solution of the differential equation $y d x+\left(x+x^2 y\right) d y=0$, is
Answer & explanation
Correct answer: option 2
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 $-\frac{1}{x y}+\log y=C$