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Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 40 maths textbook solution.

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Answer :  (c) \sec\; x

Hint: The given differential equation is linear in y.

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

Explanation: divide both sides by \cos x

\Rightarrow \frac{d y}{d x}+y \tan x=\sec x \quad\left[\frac{\sin x}{\cos x}=\tan x, \frac{1}{\cos x}=\sec x\right]

So the linear equation becomes linear in y

\begin{aligned} &I F=e^{\int \tan x d x} \\ &=e^{\log \sec x} \\ &=\sec x \end{aligned}

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