1. The problem statement, all variables and given/known data The d.e y' = (y+2x)/(y-2x) is NOT seperable, but if you use a substitution then you obtain a new d.e involving x and u, then the new d.e is seperable.... Solve the original d.e by using this change of variable method 2. Relevant equations I'm going to use the substitution that u=y/x in the form y=ux 3. The attempt at a solution y' = (y+2x)/(y-2x) let y=ux then y' = (ux+2x)/(ux-2x) y'(ux-2x) - (ux+2x) = 0 <--- thus it is seperable So I can say d/dx((ux^2)/2 - x^2) - d/dx((ux^2/2) + x^2) = 0 Putting it all together d/dx[(ux^2)/2 - x^2 - (ux^2)/2 - x^2] = 0 d/dx (-2x^2) = 0 Well that is where I am stuck, how do I solve it from there and what am I trying to get because I've changed the d.e so I'm not sure how the answer from the new d.e will help me find a solution to the original one?