Differential equation solution basic

[nanda sinha]

Ok so I tried to solve the following differential equation for y by every method (variable separable method/making to variable separable method technique/putting y/x=other variable/making homogeneous to solve equation to get y/x ).But I think I can't solve this particular equation by these methods.

y(1+xy)dx + x(1-xy)dy =0

 

[lurflurf]

change variables
u=xy
v=x/y
or use integrating factor
1/(xy)^2