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Math Help - d'Alembert's formula

  1. #1
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    d'Alembert's formula

    Good morning all, I am stuck on this question.

    Use d'Alembert's formula to write u(x,t) = x-at in the form u(x,t)=f(x+ct)+g(x-ct).

    I don't know how to do this so any help would be very nice.
    Thanks.
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  2. #2
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    Re: d'Alembert's formula

    Two thoughts. First, if you allow that c = a, then you already have the form. Second, if you let

    k_1(x+ct) + k_2(x-ct) = x - at.

    If you expand and equate like terms, you'll find two equations for k_1 and k_2.
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  3. #3
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    Re: d'Alembert's formula

    If I were you, I would start by stating d'Alembert's formula as clearly as possible.
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