Question

The integrating factor of the differential equation $x\frac{dy}{dx}+xy\cot x=0$ is $(x\ne 0)$

• A. $\cos x$
• B. $\sin x$
• C. $\sec x$
• D. $\tan x$

Answer 1

The correct option is B $\sin x$

$x\frac{dy}{dx}+xy\cot x=0\Rightarrow \frac{dy}{dx}+y\cot x=0$
Integrating factor
$=e^{\int \cot xdx}=e^{\ln \sin x}=\sin x$