(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 thats 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?

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# U-Substitution, can't figure out where the answer comes from?

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