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Help Me Factor This PDE

  1. Oct 7, 2011 #1
    1. The problem statement, all variables and given/known data

    [tex] u_{xxx} - 3u_{xxy} + 4u_{yyy} = e^{x+2y} [/tex]

    3. The attempt at a solution

    Ok so I tried doing the following to solve the homogeneous equation
    \begin{align*}

    u_{xxx} + u_{xxy} - 4u_{xxy} + 4_{yyy} = 0 \\

    [d^{2}x(dx -dy) - 4dy(dx + dy)(dx -dy)]u = 0 \\

    [(dx - dy)[d^{2}x - 4dxdy - 4d^{2}y]u = 0 \\

    (dx -dy)(dx - (2+ /sqrt{5})dy)(dx - (2 - /sqrt{5})dy)u = 0

    \end{align*}

    Is this correct? Seems way too hard... I'm sure I did something incorrectly.
    Thanks!
     
  2. jcsd
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