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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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