Help Me Factor This PDE

1. Oct 7, 2011

NeedPhysHelp8

1. The problem statement, all variables and given/known data

$$u_{xxx} - 3u_{xxy} + 4u_{yyy} = e^{x+2y}$$

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!