1. The problem statement, all variables and given/known data If y(1+x2) dy/dx = 2x (1-y2), prove that (1+x2)2(1-y2)=A, where A is constant. 2. Relevant equations Separable equations 3. The attempt at a solution Separate the terms: y/(1-y2) dy = 2x/(1+x2) dx Integrating both sides will get: ∫ y/(1-y2) dy = ∫ 2x/(1+x2) dx Use substitution method for ∫ y/(1-y2) dy: u = 1-y2 du = -2y dy -du/2 = y dy ∫ -u/2 du = -1/2 ∫ u du = (-1/2)*(u2/2) = -u2/4 + C = -(1-y2)2/4 Use substitution method for ∫ 2x/(1+x2) dx: u= 1+x2 du = 2x ∫ 1/u du = ln u + C = ln (1+x2) Putting them back together will get: -(1-y2)2/4 = ln (1+x2) I'm pretty much unable to continue from here.