Question

The integrating factor of the differential equation $\cos x\left(\frac{dy}{dx}\right)+y\sin x=1$ is

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

Answer 1

The correct option is A $\sec x$

The given differential equation is
$\cos x\left\{\frac{dy}{dx}\right\}+y\sin x=1$
$\Rightarrow \frac{dy}{dx}+y\frac{\sin x}{\cos x}=\frac{1}{\cos x}$
$\therefore IF=e^{\int \frac{\sin x}{\cos x}dx}=e^{\log \sec x}=\sec x$