The solution of the differential equation $cos x\, sin y \, dx +sinx \, cos ydy =0$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\sin x \sin y = C$, where C is a constant
$\cos x\sin y dx +\sin x \cos ydy =0$
$\cos x\sin ydx=-\sin x \cos ydy$
$\int-\cot xdx=\int\cot y dy$
so $-\log\sin y=\log\sin x+\log C$
$⇒\sin x \sin y = C$