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## Homework Statement

Simply enough, solve the following using U-Substitution.

dy/dx = y

^{2}-2y+1

and the answer key provides

y = 1+(x+C)

^{-1}

**2. The attempt at a solution**

I know how to do this, I thought. But I'm just spinning my wheels and need somebody to show me my error...

I tried moving around the dy/dx parts, so that I eventually ended up with

dx=dy/(y

^{2}-2y+1)

which simplified to

x=ln(y

^{2})2y-ln(2y)2+y, but that's not right, unless I'm missing some kind of simplification?

Honestly, I have no idea where the textbook got the answer. Any tips? What am I doing wrong?