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What am I doing wrong? Solving first order DE's

  1. Jan 19, 2009 #1
    What am I doing wrong?? Solving first order DE's

    1. The problem statement, all variables and given/known data
    Solve the following first order differential equation:
    ty' + (t+1)y = t; y(ln 2) = 1, t > 0


    2. Relevant equations



    3. The attempt at a solution
    I try to solve this using the method of integrating factors. First I divide the equation by t to get:

    y' + [(t+1)/t]y = 1

    So following from this I find the integrating factor u(t) = t*e^t

    So to solve this I just take an integral of both sides of equations to get:

    y*t*e^t = e^t(t-1) + C

    Is this right? I now just have to solve for y, and then plug in for the initial values to get C. But the answer I get does not match my book's answer! Can anyone show me what I did wrong here? Thanks
     
  2. jcsd
  3. Jan 19, 2009 #2
    Re: What am I doing wrong?? Solving first order DE's

    I get the same. What is the book's answer?
     
  4. Jan 19, 2009 #3
    Re: What am I doing wrong?? Solving first order DE's

    The book says the answer is:

    y = (t - 1 + 2e^(-t)) / t, where t cannot equal 0.
     
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