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Science & engineering math: integro-differential equation

  1. Mar 18, 2012 #1
    1. The problem statement, all variables and given/known data

    [itex]\int[/itex] y'(u)y(t-u)du = 24t3
    The integral goes from t (top) to 0 (bottom)
    With y(0) = 0

    2. Relevant equations

    I want to say it kind of looks like a convolution problem
    [itex]\int[/itex] f(u)g(t-u)du
    The integral goes from t (top) to 0 (bottom)

    3. The attempt at a solution
    I have no idea...
     
  2. jcsd
  3. Mar 18, 2012 #2
    When you see a convolution in a homework problem, you should immediately think of a transform that reduces it to a multiplication. This transform can even handle the derivative easily...
     
  4. Mar 18, 2012 #3
    Well if it is convolution then it would just be
    F(s)*G(s)
    But I was more concerned about whether or not it actually was convolution. Because its y' and y, and those are both completely different, then it would be convolution then?
    So I would need to take the Integral of y'(u) and y(t-u) then? And the integral of 24t3?
     
  5. Mar 18, 2012 #4
    it is a convolution between to functions, i.e., y'(t) and y(t), their Laplace transform are related, because one is the derivative of the other. So there is only one F(s) to solve for, the other is simply related to this one.
     
  6. Mar 19, 2012 #5
    Okay, understandable...but how do I start the problem? I'm still confused about how to start...
     
  7. Mar 19, 2012 #6

    Ray Vickson

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    What is the Laplace transform of a convolution?

    RGV
     
  8. Mar 19, 2012 #7
  9. Mar 20, 2012 #8

    HallsofIvy

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    So "start" by taking the Laplace transform of both sides!
     
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