Question

If $\sin x$ is an intergrating factor of the differential equation $\frac{dy}{dx}+Py=Q$, then P can be

• A. $\log \sin x$
• B. $\cot x$
• C. $\sin x$
• D. $\log \cos x$

Answer 1

The correct option is B $\cot x$

Integrating factor of the differential equation $\frac{dy}{dx}+Py=Q$ is given by

$I.F=e^{\int P\left(x\right)dx}$
$\Rightarrow \sin x=e^{\int P\left(x\right)dx}$
$\Rightarrow \log \sin x=\int P\left(x\right)dx$
$\Rightarrow P\left(x\right)=\frac{d}{dx}\log \sin x$
$\Rightarrow P=\frac{1}{\sin x}\cos x=\cot x$