Question

The solution of the differential equation $ydx+(x+x^{2}y)dy=0$ is:
(where $C$ is integration constant)

• A. $-\frac{1}{xy}=C$
• B. $-\frac{1}{xy}+\ln |y|=C$
• C. $\frac{1}{xy}+\ln |y|=C$
• D. $\ln |y|=Cx$

Answer 1

The correct option is B $-\frac{1}{xy}+\ln |y|=C$

$ydx+xdy+x^{2}ydy=0\Rightarrow d\left(xy\right)+x^{2}ydy=0$
On dividing both sides by $x^2{y}^2$ we have:
$\frac{d\left(xy\right)}{x^2{y}^2}+\frac{1}{y}dy=0$
$\Rightarrow -\frac{1}{xy}+\ln |y|=C$