General Solution for 2nd Order PDE: Is it Possible?

[Jhenrique]

Hellow everybody!

A simple question: exist a general formulation, a solution general, for a PDE of order 2 like:
$au_{xx}(x,y)+2bu_{xy}(x,y)+cu_{yy}(x,y)+du_x(x,y)+eu_y(x,y)+fu(x,y)=g(x,y)$
?

The maple is able to calculate the solution, however, is a *monstrous* solution!

 

[MathematicalPhysicist]

With a suitable transformation you can change it to one of the canonical representations of pdes (parabolic,hyperbolic and elliptic) and solve it.

 

[Jhenrique]

With a suitable transformation you can change it to one of the canonical representations of pdes (parabolic,hyperbolic and elliptic) and solve it.

This transformation consists in eliminate the mixed and linear terms? Resulting an equation of kind:

$Au_{xx}(x,y)+Cu_{yy}(x,y)+Fu(x,y)=g(x,y)$

?