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Partial Differential equation problem

  1. Dec 7, 2005 #1
    let be the function U=U(x,y) satisfying:
    [tex]U_{x}=(a/\epsilon)^{y}y [/tex] and [tex]U_{y}=(a/\epsilon)^{x}x[/tex] (1)
    where we have introduced the notation [tex]U_{i}=dU/di [/tex] i=x,y then from expression (1) we could construct the differential equation:
    [tex]xU_{x}-yU_{y}=0 [/tex] (2)
    from (2) we could construct the solution to obtain U, my problem is how to obtain U so its derivatives respect to x and y give the result in (1)
     
    Last edited: Dec 7, 2005
  2. jcsd
  3. Dec 7, 2005 #2

    Tide

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    How does (2) follow from (1)?
     
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