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The solution of the PDE

  1. Jul 10, 2010 #1
    find the general solution of yux+xuy=yu+xex ( the solution is in the form of u(x,y)=yex+f(y2-x2)ex )
    if at first the value of u(x,y) on the upper half of hyperbola (that is y>=1) has been given as φ,show that if φ has not been given as a special form there is no solution.find that special form of φ and show there is infinite solution in this situation.
     
    Last edited: Jul 10, 2010
  2. jcsd
  3. Jul 10, 2010 #2
  4. Jul 10, 2010 #3
    thanks for your advice
    i tried the method of characteristics,but i can not find the solution :blushing:
     
  5. Jul 10, 2010 #4

    hunt_mat

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    Homework Helper

    The characteristic equations are
    [tex]
    \dot{x}=y,\quad\dot{y}=x,\quad\dot{u}=yu+xe^{x}
    [/tex]
    then the characteristic are given as [tex]dy/dx=x/y[/tex]. Then this integrates up to [tex]f(x,y)=C[/tex]. Then use [tex]du/dx=\dot{u}/\dot{x}[/tex] and integrate up.

    Mat
     
  6. Jul 12, 2010 #5
    i found the general solution of the equation. thanks for your helps
    but i can't understand anything rest of the question.i am waiting for your helps.
     
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