# 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:

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

?