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Help with ODE

  1. Jun 18, 2011 #1
    I need help with an initial value problem,

    ty' + (t+1)y= t; y (LN 2)= 1

    I divided t and have u(t) as exp Integral of t+1/1 => e^t +t

    Multiplied this to the original equation to get

    (e^t +t)y' + ((t+ 1)/t) *y *(e^t +t) = (e^t +t)

    How can I integrate the above? Are my steps so far correct?

    Thanks
     
  2. jcsd
  3. Jun 19, 2011 #2
    ( e^t + t ) isn't correct !
     
    Last edited: Jun 19, 2011
  4. Jun 19, 2011 #3
    So, you are trying to solve using linear method?
     
  5. Jun 19, 2011 #4

    HallsofIvy

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    Staff Emeritus
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    You mean that, to find an integrating factor, you integrated (t+1)/t which is the same as 1+ 1/t. From that you get ln(u)= t+ ln(t), [itex]u= e^{t+ ln(t)}= e^t*e^{ln t}= te^t[/itex], NOT [itex]e^t+ t[/itex]

    The whole point of the integrating factor is that the left side should be equal to
    ((e^t+ t)y)'- and it isn't!

     
  6. Jun 19, 2011 #5
    Thanks for all the feedback.

    @halls- thanks, te^t did it for me, problem solved.
     
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