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Math Help - d'alembert solution Help

  1. #1
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    Question d'alembert solution Help

    Hi I have been trying to figure out how this method works.

    Searched the forum but got no results. Have attached an example Im trying to do. If someone could show me it would be great.

    Or even show me a similar example worked out.

    Thanks in advance!



    Edit: I am trying another question
    u_tt = u_xx
    u( x, 0) = 0 = f(x) ?
    u_t( x,0) = xe^-(x^2) = g(x)?

    So as f(x) = 0 can I just figure out the ingegral of g(x) with limits (x+ct) and (x-tc)

    The answer is supposed to be 11 but I just get

    1/4 [ -e^(x+t)^2 + e^-(x-t)^2]




    I use the formula and as f(x) = 0
    Attached Thumbnails Attached Thumbnails d'alembert solution Help-example.gif  
    Last edited by Niall101; May 14th 2010 at 06:55 PM.
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  2. #2
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    Quote Originally Posted by Niall101 View Post
    Hi I have been trying to figure out how this method works.

    Searched the forum but got no results. Have attached an example Im trying to do. If someone could show me it would be great.

    Or even show me a similar example worked out.

    Thanks in advance!



    Edit: I am trying another question
    u_tt = u_xx
    u( x, 0) = 0 = f(x) ?
    u_t( x,0) = xe^-(x^2) = g(x)?

    So as f(x) = 0 can I just figure out the ingegral of g(x) with limits (x+ct) and (x-tc)

    The answer is supposed to be 11 but I just get

    1/4 [ -e^(x+t)^2 + e^-(x-t)^2]




    I use the formula and as f(x) = 0
    The answer can't be 11! If the answer was u(x,t) = 11, then u_t(x,t) = 0 always and so u_t(x,0) = 0 and not u_t(x,0) = xe^{-x^2} \ne 0 for all x. Your answer (almost) is correct

     <br />
u(x,t) = \frac{1}{4} \left( e^{-(x-t)^2} - e^{-(x+t)^2}\right)<br />

    It satisfies both the PDE and the initial conditions.
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  3. #3
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    Hey Thanks for that. Someone on the college forum said they got 11 for the answer which threw me way off.
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