Ask for different ways to solve $(x+y)dy+(y+1)dx=0$ $(x+y)dy+(y+1)dx=0$
Rewrite the equation to 
$\frac{dx}{dy}+\frac{x}{y+1}=\frac{-y}{y+1}$ 
I can use used the integrating factor $μ(y)=e^{-\int\frac{1}{y+1}dy}$ to solve it.
The answer is $x=\frac{-y^2}{2(y+1)}+\frac{C}{y+1}$
I'm curious that are there any other methods to solve this ODE. I am asking for a different method because sometimes I am not able(or haven't enough time, this one costs me about half an hour to solve it ) to  rewrite the equation into a proper form. So, if I could obtain other methods to solve this kind of ODEs, I may have more chances to solve it in a exam.

See that we can write as
$$(x+y)dy+(y+1)dx=0$$
$$xdy+ydx+ydy+dx=0$$
$$d(xy)+ydy+dx=0$$ now just integrate.
