I'm solving the following differential equation: $$x+xy+y'(y+xy)=0$$ So far I've tried to rewrite it somehow to separate variables but it didn't really work. I've got a remark to introduce a substitution of some kind but couldn't think of it right away.
How do you conclude what a substitution should be in such cases?
Here's equivalent form of the eq. above: $$(1+y)xdx+(1+x)ydy=0$$