The integrating factor of differential equation $\cos x \frac{dy}{dx} + y \sin x = 1$ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\sec x$ ##
Given that, $\cos x \frac{dy}{dx} + y \sin x = 1$
On dividing both sides by $\cos x$, we get
$⇒\frac{dy}{dx} + y \tan x = \sec x \quad \left[ ∵\frac{\sin x}{\cos x} = \tan x, \frac{1}{\cos x} = \sec x \right]$
On comparing $\frac{dy}{dx} + Py = Q$
Here, $P = \tan x$ and $Q = \sec x$
$∴\text{I.F.} = e^{\int P \, dx} = e^{\int \tan x \, dx} = e^{\log \sec x}$
$= \sec x \quad [∵ e^{\log x} = x]$