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Math Help - how do i show something is a solution without solving it? 2nd order DE

  1. #1
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    Question how do i show something is a solution without solving it? 2nd order DE

    the wave equation

    δ2y/δx2 = (1/c2)(δ2y/δt2)

    show y(x,t) = f(x-ct)+g(x+ct) is a solution explicitly


    please show me how, don't just say "substitution"
    Last edited by ouchimdead; June 17th 2012 at 06:08 AM.
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  2. #2
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    Re: how do i show something is a solution without solving it? 2nd order DE

    Quote Originally Posted by ouchimdead View Post
    don't just say "substitution"
    Ahem...

    Anyway, just in case a picture helps...



    ... where (key in spoiler) ...

    Spoiler:


    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x and t in turn), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).



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