Solve 3x^2-y^2)dx+(xy-x^3y^{-1})dy=0 through homogenous equations i've gotten to y(y^2-3x^2)/x(y^2-x^2) but don't know what to do from there

First you have to make the diff equation exact by multiplying by an integrating factor.

The integrating factor will be in the form: 

This gives:


Now set partial derivatives equal to find a,b.





Setting coefficients equal we have:


Solving this system of 2 equations yields:


Now you have an exact diff equation: 


The solution is:






h(y) and h(x) are constants in terms of the specified variable.
By equating the 2 integrals, you can see that


Finally, the general solution is: