I'm self teaching and working though Cliff's quick review on Differential Equations. Asked to solve the following one
$$x(1 - \sin y) \, dy = (\cos x - \cos y - y) \, dx$$
The answer I got was $$\sin x - x\cos y - xy = c$$ the book says $$xy + x\cos y - \sin x = c$$
I feel like I'm asking a probably obvious question, but can someone confirm my answer is ok? My rationale is it's fine as the constant of integration could be negative, therefore negating the terms on the LHS.