Question

Integrating factor of differential equation $\cos x\frac{dy}{dx}+y\sin x=1$ is

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

Answer 1

The correct option is C $|\sec x|$

$\cos x\frac{dy}{dx}+y\sin x=1$
$\Rightarrow \frac{dy}{dx}+y\frac{\sin x}{\cos x}=\sec x$
$\therefore \text{I.F}=e^{\underset{}{\overset{}{\int }}Pdx}$
Now, $\underset{}{\overset{}{\int }}Pdx=\underset{}{\overset{}{\int }}\frac{\sin x}{\cos x}dx=-\ln |\cos x|$
So. $I.F=e^{\ln |\sec x|}=|\sec x|$