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Integrating factor confusion

  1. Sep 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Solving this differential equation
    ty' + 2y = t^2 - t + 1

    2. Relevant equations
    Its linear so i set it up in linear form
    y' + y(2/t) = t - 1 +1/t


    3. The attempt at a solution

    the integrating factor (u) = e ^ integral (ydt) = e^ integral (2dt/t)...
    Here's the question, my book says u = t^2, and i just can't figure out how e ^ integral (2dt/t) is t^2

    Its probably some stupid thing that i'm getting stuck on, thanks.
    I know how to do this afterwards, i just can't for the life of god figure out why u = t^2
     
  2. jcsd
  3. Sep 19, 2009 #2
    [tex]u = e^{\int\frac{2dt}{t}} = e^{2\ln t} = (e^{\ln t})^2[/tex]
     
  4. Sep 19, 2009 #3
    oh wow i thought u could bring the 2 out front.... thanks for clearing that up
     
  5. Sep 19, 2009 #4
    Thanks Bohrok, I thought that was were is was coming from also but was having trouble typing it out.

    Matt
     
    Last edited: Sep 19, 2009
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