Solving a first-order nonlinear ordinary differential equation

xy' + y^2 = 1, y(1) = 0

xy' = 1 - y^2

dy / (1-y^2) = dx / x

Need to take into account the possiblity of having "divided away" solution. We check if = +/- 1 are solutions by inserting them into the equation. They aren't solutions.

Moving on. We get (1/2)ln|1+y| - (1/2)ln|1-y| = ln|x| + C

This is where I'm stuck. Since we have the initial condition y(1) = 0 we need to figure out C in this step before moving on, right? What I've done in previous exercises is to isolate y and take it from there, but I don't know how to do it in this case. I've tried doing the following:

ln| (1+y) / (1-y) | = ln|x|^2 + 2C

Multiply with e and we get

| (1+y) / (1-y) | = x^2 + e^(2C)

But, well, I can't get it to work out.