Find the general solution of $(x + \sin{x} +\sin{y})\ \textrm{d}{x} + \cos{y}\ \textrm{d}{y}=0$ I have tried to make this equation seperable, homogeneous, exact and use integrating factors and nothing seems to be working. Could you tell me what form to use?

if you multply through by $e^x$ you have an exact diff eq.
$(x e^x + e^x \sin x + e^x \sin y)dx + (e^x \cos y) dy = 0\\
\nabla (x e^x-e^x + \frac 12 e^x \sin x - \frac 12 e^x \cos x + e^x \sin y) = (x e^x + e^x \sin x + e^x \sin y)dx + (e^x \cos y) dy\\ 
x e^x-e^x + \frac 12 e^x \sin x - \frac 12 e^x \cos x + e^x \sin y = C\\
-x + 1 - \frac 12 \sin x + \frac 12 \cos x +Ce^{-x} = \sin y\\
y = \arcsin( 1-x - \frac 12  \sin x + \frac 12 \cos x +Ce^{-x})$
