Question

The integrating factor of linear differential equation $\frac{dy}{dx}+y\sec x=\tan x$ is:

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

Answer 1

The correct option is C $\sec x+\tan x$

Given, $\frac{dy}{dx}+y\sec x=\tan x$

Here $P=\sec x$

$\therefore$ Integrating factor $=e^{\int Pdx}$

$=e^{\int \sec xdx}$

$=e^{\log (\sec x+\tan x)}$

$=\sec x+\tan x$