Question

Solve $(xy-1)\frac{dy}{dx}+y^2=0$.

• A. $xy+\log x=C$
• B. $xy+\log y=C$
• C. $xy-\log y=C$
• D. $xy-\log x=C$

Answer 1

The correct option is C $xy-\log y=C$

Given, $(xy-1)\frac{dy}{dx}+y^2=0$

It can be written as

$xydy+y^{2}dx-dy=0$

On multiplying by $\frac{1}{y}$, we get

$xdy+ydx-\frac{1}{y}dy=0$

$\Rightarrow d\left(xy\right)-\frac{1}{y}dy=0$

On integrating, we get

$\Rightarrow \int d\left(xy\right)-\int \frac{dy}{y}=0$

$\Rightarrow xy-\log y=C$