1. The problem statement, all variables and given/known data Solve the separable equation 2. Relevant equations dy/dx = 1-y^2 3. The attempt at a solution dy/dx = 1-y^2 1/(1-y^2) dy = dx [Partial fraction] A/(1-y) + B/(1+y) = 1/(1-y^2) A + Ay + B - By = 1 y^1: A - B = 0 y^0: A + B = 1 => A=B=1/2 => (1/2)/(1-y) dy + (1/2)/(1+y) dy = dx ln|1-y| + ln |1+y| = 2x + C ln|1-y^2| = 2x + C 1-y^2 = De^(2x) y = sqrt(1 - De^(2x)) This answer is wrong according to two different books (without explanation) that i have. The correct answer should be y = (De^(2x) - 1)/(De^(2x) + 1) Is partial fraction wrong way to go? Have I made a wrong turn along the way with the algebra? I do have big problems when i comes to solve nonlinear integrals, a tip along the way would be very appreciated!