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Short-answer question on characteristics of p.d.e

  1. May 26, 2015 #1
    1. The problem statement, all variables and given/known data
    ut − 2ux =1/ u;
    what expressions are constant along the equations's characteristics?
    2. Relevant equations
    3. The attempt at a solution

    Am I right?
    dt=dx/(-2)=du/(-1/u), -2t=x=u2;
    u=sqrt(x); u=sqrt(-2t) are constant.
     
  2. jcsd
  3. Jun 1, 2015 #2

    MarcusAgrippa

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    I think that they may want a slightly more general answer. Have you quoted the question precisely as it was stated?
     
  4. Jun 1, 2015 #3
    Oh yes, the question is stated just like there...
     
  5. Jun 2, 2015 #4

    MarcusAgrippa

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    Gold Member

    Then, apart from the fact that you have ignored the second branch of the square root function, your answer is correct. It may be better to quote the solution function u(x,t) in implicit form rather than to solve it explicitly for u. That way you include both branches of the square root function.
     
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