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Please Solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 15 Maths Textbook Solution.

Answers (1)

Answer:  2 y \cos x=\cos 2 x+C

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

Give:  \begin{aligned} &\frac{d y}{d x}=y \tan x-2 \sin x \\ & \end{aligned}

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

 =\frac{d y}{d x}+P y=Q

\begin{aligned} &P=-\tan x, Q=-2 \sin x \\ & \end{aligned}

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

=e^{\int 1 d x} \\

=e^{x} \\

=y I\! f=\int Q I\! f d x+C \\

=y \cos x=-\int 2 \sin x \cos x d x+C

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

=y \cos x=\frac{\cos 2 x}{2}+C \\

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

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