I'm currently trying to solve the differential equation: $$x^2y'^2-2(xy-4)y'+y^2=0,$$ but up to now I've had no succes. I rewrote it as
hoping that the equation would become seperable. Unfortunately this only works well for linear equations. So I got: $$x^2v'^2-4vv'x+4v^2+8xv'-8v=0.$$ This seems pretty hard to solve. I don't know if there is a better substitution, or simply a better method to solve this one ?