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Homework Help: Show that the function is a solution of the wave equation

  1. Jul 17, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that the function is a solution of the wave equation utt = a2uxx.

    u = (t)/(a2t2-x2)

    2. Relevant equations
    Quotient rule
    (f/g)' = (g*f ' - f*g') / g2

    3. The attempt at a solution
    I began with the first and second partials of u with respect to x:
    http://imageshack.com/a/img661/7646/Xnbsd2.png [Broken]
    I'm fairly confident that this part is correct, because I checked it with an online calculator.
    Then I did the first partial of u with respect to t:
    http://imageshack.com/a/img537/4254/5hYVrv.png [Broken]
    Then the second partial:
    http://imageshack.com/a/img537/7426/Xr15AC.png [Broken]

    So I'm getting -utt = a2uxx. I've done this several times now, and I keep getting the extra negative sign in utt. I can't figure out where it's coming from; I'm sure it's some silly mistake with a dropped sign somewhere. I'd appreciate the help of anyone who could help me spot it.
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Jul 17, 2015 #2


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    Homework Helper

    *Edit* Sorry I misspoke on the initial response.
    It looks like in your simplification of the second partial wrt t, you cancel a negative sign incorrectly.
    Last edited: Jul 17, 2015
  4. Jul 17, 2015 #3
    Ah, I see it now. No idea why I kept thinking I could do that; I must have done this problem five or six times and did that every time. Thanks for your help!
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