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