Question

If $\cos x$ is an intergrating factor of the differential equation $\frac{dy}{dx}+Py=Q$ the $P=$

• A. $\tan x$
• B. $-\cot x$
• C. $-\tan x$
• D. $\cot x$

Answer 1

The correct option is C $-\tan x$

Given Integrating Factor$=\cos x$

$\Rightarrow P=\frac{\frac{d}{dx}\left(\cos x\right)}{\cos x}$

$\Rightarrow P=\frac{-\sin x}{\cos x}=-\tan x$

$\therefore P=-\tan x$