Answer
\[\sin x\cos y=C\]
Work Step by Step
$\large\frac{dy}{dx}=\large\frac{\cos(x-y)}{\sin x\sin y}-\small1$ ___(1)
$\large\frac{dy}{dx}=\frac{\cos x\cos y+\sin x\sin y}{\sin x\sin y}-1$
$\large\frac{dy}{dx}=\frac{1}{\tan x\tan y}$
Separating variables, $\;\;\tan y\; dy=\cot x\;dx$
Integrating,
$K+\int\tan y\; dy=\int\cot x\;dx$
$K$ is constant of integration
$K-\ln|\cos y|=\ln |\sin x|$
$K=\ln|\sin x\cos y|$
$\ln C=\ln|\sin x\cos y|$
Where $K=\ln C$
$C=\sin x\cos y$
Solution of (1) is $\;\;\sin x\cos y=C$
