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Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 17 textbook solution.

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Answer : y\sec x = x+c

Hint : To solve this equation we use e^{\int P d x}  formula.

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

Solution : \frac{d y}{d x}+Py=Q

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

     \begin{aligned} &I f=e^{\int P d x} \\ \end{aligned}

     \begin{aligned} &=e^{\int \tan x d x} \\ \end{aligned}

     \begin{aligned} &=e^{\log \sec x} \\ \end{aligned}

     \begin{aligned} &=\sec x \\ \end{aligned}

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

     \begin{aligned} &=y \sec x=\int \sec x \cos x d x \\ \end{aligned}

    \begin{aligned} &=y \sec x=\int \frac{1}{\cos x} \cos x d x \\ \end{aligned}

    \begin{aligned} &=y \sec x=\int 1 d x \\ \end{aligned}

    \begin{aligned} &=y \sec x=x+C \end{aligned}


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