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Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 3 maths textbook solution.

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Answer : (b)\sec\; x

Hint :  \frac{d y}{d x}+P(x) y=Q(x) \text { then } I F=e^{\int P(x) d x} when the ifferential equation is linear in y

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

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

The given differential equation is linear in y

\begin{aligned} &I F=e^{\int \frac{\sin x}{\cos x} d x} \\ &=e^{\int \tan x d x} \\ &=e^{\ln \sec x} \\ &=\sec x \end{aligned}


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