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

  1. Nov 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Simply enough, solve the following using U-Substitution.

    dy/dx = y2-2y+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/(y2-2y+1)
    which simplified to
    x=ln(y2)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?
     
  2. jcsd
  3. Nov 5, 2011 #2
    Can you factor y^2-2y+1?
     
  4. Nov 5, 2011 #3
    That would be it! I knew it was something simple, thanks!
     
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