The integrating factor of differential equation cos x d y d x + y sin x = 1 is:

Question

The integrating factor of differential equation $\cos x \frac{d y}{d x} + y \sin x = 1$ is:

Smart Achievers · Accepted Answer

(3)

Ans. $\sec x$

Explanation:

Given that,

$\cos x \frac{d y}{d x} + y \sin x = 1$

$\Rightarrow$ $\frac{d y}{d x} + y \tan x = \sec x$

Here, $P = \tan x$ and $Q = \sec x$

$IF = e^{\int P d x} = e^{\int \tan x d x} = e^{\log \sec x}$

$\Rightarrow$ $= \sec x$

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