Q. The 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\$
Explanation
(a)
Given, $\frac{dy}{dx}\tan y = \sin(x + y) + \sin(x - y)$
$\Rightarrow$ $\frac{dy}{dx}\tan y = 2\sin x\cos y$
$\Rightarrow$ $\tan y\sec y\ dy = 2\sin x\ dx$
$\Rightarrow$ $\sec y = - 2\cos x + c$ [integrating]
$\Rightarrow$ $\sec y + 2\cos x = c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.