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Homework Help: Solve homogeneous first order PDE's

  1. Sep 10, 2006 #1
    [tex]u_x+u_y+u=e^{x+2y}, y(x,0)=0[/tex]

    I have no idea how to do this. We were only taught how to solve homogeneous first order PDE's.
     
  2. jcsd
  3. Sep 10, 2006 #2

    Dr Transport

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    try separating variables...
     
  4. Sep 10, 2006 #3
    What do you mean?
     
  5. Sep 13, 2006 #4
    I am getting nowhere with this. I tried using the method of characteristics, but it doesn't work out.
     
  6. Sep 13, 2006 #5

    J77

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    Write [tex]u(x,y)=X(x)Y(y)[/tex], plug this into you equation and...

    Note also: [tex]e^{x+2y}=e^xe^{2y}[/tex]
     
  7. Sep 13, 2006 #6
    How do you know that u actually can be written as X(x)Y(y)?
     
  8. Sep 13, 2006 #7
    I think that it's more or less an assumption we make when dealing with homogenous PDEs, but I'm probably completely wrong on this.
     
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