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Explain solution RD Sharma class 12 Chapter 21 Differential Equation exercise 21.10 question 17

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Answer:  y \sec x=x+C

Hint: To solve this equation we use  e\int P dx  formula.

Give:  \frac{d y}{d x}+y \tan x=\cos x

Solution:  \frac{d y}{d x}+P y=Q

\begin{aligned} &P=\tan x, Q=\cos x \\ \end{aligned}

\text { If }=e^{\int P d x} \\

=e^{\int \tan x d x} \\

=e^{\log \sec x} \\

=\sec x

\begin{aligned} &=y I f=\int Q I f d x+C \\ &=y \sec x=\int \sec x \cos x d x \\ &=y \sec x=\int \frac{1}{\cos x} \cos x d x \\ &=y \sec x=\int 1 d x \\ &=y \sec x=x+C \end{aligned}

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