I'm a little rusty with partial fractions, and I can't seem to find my error once I get up to that point. 1. The problem statement, all variables and given/known data dy/dx = (y^2 - 1) / x 2. Relevant equations 3. The attempt at a solution Cross-mutliply x dy = (y^2 - 1) dx Divide by the appropriate terms dy / (y^2 - 1) = dx / x So I'm integrating 1 / (y^2 - 1) dy and 1/x dy Obviously, the integral of 1/x is ln|x| + c, but I'm having trouble with integrating the y terms. This is what I did so far. A / (y + 1) + B/ (y - 1) = 1 / (y^2 - 1) Ay - A + By + B = 1 Combine the y terms and constant terms A + B = 0 (Since there's no y term) -A + B = 1 2B = 1 B = 0.5 So I integrate 0.5 / (y - 1) and get 0.5*ln|y - 1| So that means 0.5*ln|y - 1| = 1/|x| + c ln|y - 1| = 2/x + c y - 1 = e^(2/x + c) y - 1 = e^(2/x) * e^c (which is just a constant) y = ce^(2/x) + 1 But the thing is that I checked online to find out how to integrate the y term, and found this: http://calc101.com/partial_1.html My question is: Why does 1 / (y + 1)(y - 1) get split up into 1/(2y - 2) and 1/(2y + 2)? Also, why are they subtracting those 2 terms rather than adding them?