General solution to PDE

1. Jan 16, 2014

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!

Last edited: Jan 16, 2014
2. Jan 17, 2014

MathematicalPhysicist

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

3. Jan 25, 2014

Jhenrique

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

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

?