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Math Help - Triple Integral - Volterra equation problem

  1. #1
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    Triple Integral - Volterra equation problem

    Here's the problem:

    y'''(x) = f(x) subject to the conditions y(0)=y(1)=y(2)=0.

    Perform three integrations to show that a solution may be written

    y(x) = \int_{0}^{2}L(x,t)f(t)dt

    Determine L(x,t).

    My attempt:

    After triple integration I get

    y(x) = Ax +Bx^2 +\frac{1}{2}\int_{0}^{x}(x-t)^2f(t)dt

    where A and B are constants which I've determined but won't write here.

    Anyway, I don't see how this can be converted to find the desired L(x,t)
    (I'm assuming my triple integration is correct- I think it is)
    Last edited by mr fantastic; December 25th 2010 at 06:03 PM. Reason: Restored deleted question. User banned.
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  2. #2
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    Quote Originally Posted by ark600 View Post
    Here's the problem:

    y'''(x) = f(x) subject to the conditions y(0)=y(1)=y(2)=0.

    Perform three integrations to show that a solution may be written

    y(x) = \int_{0}^{2}L(x,t)f(t)dt

    Determine L(x,t).

    My attempt:

    After triple integration I get

    y(x) = Ax +Bx^2 +\frac{1}{2}\int_{0}^{x}(x-t)^2f(t)dt

    where A and B are constants which I've determined but won't write here.

    Anyway, I don't see how this can be converted to find the desired L(x,t)
    (I'm assuming my triple integration is correct- I think it is)
    The form of your solution is correct, and if you have solve for A and B you are done!
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  3. #3
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    I couldn't see the wood for the trees: the question just asked for a solution.
    I just stick x=2 in.
    LOL
    Cheers
    Last edited by mr fantastic; December 25th 2010 at 06:32 PM. Reason: Restored deleted post. User banned.
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