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General solution to PDE

  1. Jan 16, 2014 #1
    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. jcsd
  3. Jan 17, 2014 #2

    MathematicalPhysicist

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    Gold Member

    With a suitable transformation you can change it to one of the canonical representations of pdes (parabolic,hyperbolic and elliptic) and solve it.
     
  4. Jan 25, 2014 #3
    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) ##

    ?
     
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