1. The problem statement, all variables and given/known data So the problem goes like this: Code (Text): dy/dx = ( x^2 + xy + y^2 ) / x^2 a) Show that it is a homogeneous equation. b) Let v = y/x and express the eqn in x and v c) Solve for y 2. Relevant equations (Included) 3. The attempt at a solution Code (Text): a) dy/dx = ( x^2 + xy + y^2 ) / x^2 * [(1/xy) / (1/xy)] = [(x/y) + 1 + (y/x)] / (x/y) Since RHS is expressed only in terms of y/x, therefore it is homogeneous. b) v = y/x y = vx dy/dv = x dy/dx = (dy/dv) (dv/dx) = x (dv/dx) .'.dy/dx = [(x/y) + 1 + (y/x)] / (x/y) becomes x (dv/dx) = [(1/v) + 1 + v] / (1/v) = v^2 + v + 1 dx/x = dv/(v^2 + v + 1) The problem is, when I solve by integrating both sides, I get some gibberish arctan (2v/sqrt(3) + 1)term. The solution in the book and solved on wolfram alpha is: arctan (y/x) - ln |x| = c However, this answer suggests that the equation in b) must've been dx/x = dv/(v^2 + 1) <- no v term Which is clearly not the case... What am I doing wrong??