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First order differential equation

  1. Oct 31, 2009 #1
    1. The problem statement, all variables and given/known data

    y is a function of t

    2. Relevant equations


    3. The attempt at a solution

    Considering that the equation is of the form dy/dt + p(t)y =q(t) , I have been looking for an integrating factor of the form: e^{integral[p(t)dt]}, where p(t) = ke^(-t)
    If I calculated correctly, the integrating factor I found is (-t).
    Multiplying both sides of the original equation just brought me to a new full stop.

    Thank you very much for any guidance and correction.
  2. jcsd
  3. Oct 31, 2009 #2


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    How did you calculate the integral of k*e^(-t) and get (-t)??
  4. Oct 31, 2009 #3
    Thank you!
    I ended with integrating factor y = e^{-k*e^(-t)}
    I took ln of both sides but wrote it wrongly. Nonetheless, if I get ln(y) = k*ln(t) I still don't know how to follow.
    Unless, of course, this is not right either.

    Thank you for any input.
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