The book only has one example of this and it's really confusing me. [tex](x^2+y^2)dx+(x^2-xy)dy=0[/tex] I can see that it's homogeneous of degree 2 They then let [tex]y = ux[/tex] From there they state that [tex]dy = udx+xdu[/tex] (I'm not sure where this is coming from, but can just accept it on faith if I have to) I'm fine with making the subs. [tex](x^2+u^2x^2)dx+(x^2-ux^2)(u dx+x du)=0[/tex] This is the part that really screws me up. [tex]x^2(1+u)dx+x^3(1-u)du=0[/tex] Where did the [tex]x^3[/tex] come from? All I see is [tex]x^2[/tex]. Or I guess I should ask, how did [tex]udx+xdu[/tex] become just [tex]xdu[/tex]? That would explain the [tex]x^3[/tex] they have.