Hey all, i think i'm doing most of this right, but i'm missing a coefficient somewhere when integrating or something... 1. The problem statement, all variables and given/known data Substitute v=y/x into the following differential equation to show that it is homogeneous, and then solve the differential equation. y'=(3y^2-x^2)/(2xy) 2. Relevant equations v=y/x y=xv(x) => y'=v+xv' v'=dv/dx 3. The attempt at a solution y'=(3y^2-x^2)/(2xy) divide top and bottom of right hand side by x^2 to get v's and replace y' by v+xv' v+xv'=(3v^2-1)/(2v) subtract v from both sides xv'=(3v^2-1)/(2v)-v put the lonely v on a common denominator xv'=(3v^2-1-2v^2)/(2v)=(v^2-1)/(2v) separate v's and x's (2v)dv/(v^2-1)=dx/x integrate ln|v^2-1|=ln|x|+c substitute v=y/x ln|(y/x)^2-1|=ln|x|+c simplify ln|y^2-x^2|=ln|x|+c the back of the book says the answer is |y^2-x^2|=c|x|^3. what am i doing wrong? i'm missing a 3 somewhere. i'm kinda rusty with lograthimic algebra, so all help is appreciated. i've gotten a few of these problems wrong by missing a constant or exponent on the right hand of the side of the equation after integrating.