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Q.

Integrating factor of the differential equation $\frac{d y}{d x} + y \tan x - \sec x = 0$ is

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a

$\cos x$

b

$s e c x$

c

$e^{\cos x}$

d

$e^{\sec x}$

answer is B.

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Detailed Solution

$\begin{aligned} \frac{d y}{d x} + y \tan x - \sec x = 0 \\ \frac{d y}{d x} + (\tan x) y = \sec x \end{aligned}$

I.F. $= e^{\int \tan x d x} = e^{\log \sec x} = \sec x$

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Integrating factor of the differential equation dydx+ytan⁡x−sec⁡x=0 is