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Use an integrating factor to solve

  1. Feb 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Use an integrating factor to determine the general solutions of the following differential

    dx/dt - 2/t = 2t3 + (4t2)(e4t)

    2. Relevant equations

    R(x) = e∫P(x).dx

    3. The attempt at a solution

    Usually the equation is in the form dx/dt + P(x)t = Q(x) but here I'm not sure what to do to find P(x) here as I have 1/t, t3 and t2.

    I'm also not sure how to go about finding a solution either. I know that once I have found the integrating factor, I have to multiply the original equation by R(x). After that I'm not sure what to do.
  2. jcsd
  3. Feb 23, 2014 #2
    Well, it looks like this equation is actually separable. Just move the -2/t over, and the right side will be entirely a function of t.
  4. Feb 23, 2014 #3
    I realised that whilst I was doing it, but the question specifically asks me to use an integrating factor. thanks for the reply though.
  5. Feb 23, 2014 #4


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    Here, your independent variable is ##t##. So your integrating factor is ##R=e^{\int\frac 2 t~dt}##. Evaluate that and multiply through by it.
  6. Feb 23, 2014 #5
    Oh, I see. Thanks, I was being a bit stupid there.
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