The solution of the differential equation $\cos x \sin y d x+\sin x \cos y d y=0$, is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\sin x \sin y=C$
$\cos x \sin y d x=-\sin x \cos y d y=0$
$\frac{dy}{dx}=\frac{\cos x \sin y}{-\sin x \cos y}$
$\frac{dy}{dx}=-\frac{\tan x}{\tan y}$
$\int\frac{1}{\tan y}dy=\int\frac{1}{\tan x}dx$
$\ln(|\sin x|) + \ln(|\sin y|) = C$
$\ln(|\sin x \sin y|) = C$
$\sin x \sin y = C$