Q. The solution of $\frac{dy}{dx} + 1 = cosec\ (x + y)$ is
A) $\cos{(x + y) + x = c}$
B) $\cos{(x + y = c}$
C) $\sin{(x + y) + x = c}$
D) $\sin{(x + y) + \sin{(x + y) = c}}$
Explanation
(a)
$\because\ \frac{dy}{dx} + 1 = cosec\ (x + y)$
Let $x + y = t$
and $1 + \frac{dy}{dx} = \frac{dt}{dx}$
$\Rightarrow \ \frac{dt}{cosec\ t} = dx$
$\therefore\ \int_{}^{}{\sin{t\ dt =}}\int_{}^{}{dx}$
$\Rightarrow \ - \cos{t = x - c}$
$\Rightarrow \cos{(x + y) + x = c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.