Question

If $\sin x$ is the integrating factor (I.F) of the linear differential equation $\frac{dy}{dx}+Py=Q$, then $P$ is

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

Answer 1

The correct option is D $\cot x$

$I.F=e^{\int Pdx}$

But $I.F=sinx$

$\Rightarrow sinx=e^{\int Pdx}$

Applying log on both the sides

$\Rightarrow log\left(sinx\right)=\int Pdx$

Now differentiating both the sides

$\Rightarrow P=\frac{cosx}{sinx}=cotx$