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Easy DE

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the solution of the equation

    uxy = ux

    3. The attempt at a solution

    ux = p

    py = p

    ln p = y + c*

    p = ce^y

    But them, what is u?
     
    Last edited: Oct 5, 2008
  2. jcsd
  3. Oct 5, 2008 #2

    HallsofIvy

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    Staff Emeritus
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    Well, how would you solve the ORDINARY differential equation. dp/dx= p? That's seems to me very easy. Warning: because this is NOT an ordinary differential equation, the "constant" in the solution may be a function of y. Also remember that the general solution to a partial differential equation involves unknown FUNCTIONS.
     
  4. Oct 5, 2008 #3
    Just integrate wrt. x so that

    u(x,y) = e^y Int[c(x)]dx + g(y) where c(x) and g(y) are arbitrary?
     
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