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Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 15 textbook solution.

Answers (1)

Answer : 2 y \cos x=\cos 2 x+C

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

Give : \frac{d y}{d x}=y \tan x-2 \sin x

Solution : \frac{d y}{d x}-y \tan x=-2 \sin x

                 \frac{d y}{d x}+Py=Q

                 \begin{aligned} &P=-\tan x, Q=-2 \sin x \\ &I f=e^{\int P d x} \\ &=e^{\int -\tan x d x} \\ &=\cos x \end{aligned}

                 \begin{aligned} &=y I f=\int Q I f d x+C \\ &=y \cos x=-\int 2 \sin x \cos x d x+C \\ &=y \cos x=-\int \sin 2 x d x+C \end{aligned}

                 \begin{aligned} &=y \cos x=\frac{\cos 2 x}{2}+C \\ &=2 y \cos x=\cos 2 x+C \end{aligned}

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