The integrating factor of differential equation $\frac{dy}{dx} + y \tan x - \sec x = 0$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\sec x$ ##
Given that, $\frac{dy}{dx} + y \tan x - \sec x = 0$
$\Rightarrow \frac{dy}{dx} + y \tan x = \sec x$
Which is a linear differential equation.
On comparing it with the equation $\frac{dy}{dx} + Py = Q$, we get
Here, $P = \tan x, Q = \sec x$
$\text{I.F} = e^{\int P \, dx} = e^{\int \tan x \, dx}$
$= e^{(\log \sec x)}$
$= \sec x \quad [∵e^{\log x} = x]$