Question

Solution of the differential equation $\frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y)$ is

• A. $\sec y+2\cos x=c$
• B. $\sec y-2\cos x=c$
• C. $\cos y-2\sin x=c$
• D. $\tan y-2\sec y=c$

Answer 1

Answer: (A)

$\sec y+2\cos x=c$

Given differential equation is

$\frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y)$

or $\frac{dy}{dx}\tan y=2\sin x\cos y$

or $\tan y\sec ydy=2\sin xdx$

On integrating both sides, we get

$\sec y=-2\cos x+c$

$\Rightarrow \sec y+2\cos x=c$