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First order PDE help

  1. Apr 12, 2010 #1
    I'm trying to solve this equation:

    Ux + Uy + U = e^-(x+y) with the initial condition that U(x,0)=0

    I played around and and quickly found that U = -e^-(x+y) solves the equation, but does not hold for the initial condition. For the initial condition to hold, I think there needs to be some factor of y in the equation for U, but after trying a few equations, I can't find one that satisfies both the initial condition and the equation.

    Can someone throw me a hint?

    Last edited: Apr 12, 2010
  2. jcsd
  3. Apr 12, 2010 #2


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    You might try the substitution [itex]u(x,y)=v(x,y)e^{-(x+y)}[/itex]....
  4. Apr 12, 2010 #3
    You need to variables for the plane:

    [tex]z=x+y, t=x-y [/tex]

    your equation only depends on one of them

    [tex] 2u_{,z}+u=e^{-z}[/tex]
    Last edited by a moderator: Apr 15, 2010
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