Linear partial differential eqn.

Submitted by vic777 on Sun, 09/16/2007 - 20:12.

How can I find characteristics and characteristic coordinates for:

$u_{xx}+2u_{xy}+3u_{yy}+4u_x+5u_y+u=e^x$
Note: $u_{xx}, u_{xy}, u_{yy}$ are second partial diff...
$u_x, u_y$ partial diff...