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Very simple question about differential equations, but I couldn't find anything online.

Let $f(x,z)$ be a function of two variables that satisfies:

$af+bf_x+cf_z+df_{xx}+ef_{zz}+gf_{xz}=q(x,z)$

where $q(x,z)$ is some known function, $a,b,c,d,e,g$ are constants.

How can I solve this, i.e., find an expression for $f(x,z)$ (given boundary conditions)?

Is there some reference where I can find general solution to differential equations of functions of two variables?

Pcw.
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  • didn't realize those are constants. That is a good deal easier. Perhaps someone can you give a nice recipe for determining it's type and change variables to a known solution. – muaddib May 29 '15 at 22:03
  • are $a,\cdots,g$ related i.e. It would be nice if $\left(\alpha\partial_x +\beta\partial_z +\gamma\right)^2f = af+\cdots gf_{zz}$ – Chinny84 May 30 '15 at 00:16
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    Are you familiar with the classification: parabolic, elliptic and hyperbolic PDEs? – Dmoreno May 30 '15 at 02:07
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    There is not, and cannot be, a cookbook for solving partial differential equations. –  May 30 '15 at 04:29
  • I am not familiar with parabolic, elliptic and hyperbolic, I guess I should be. Googling "Introduction to PDEs" I found some useful material, it doesn't really seem to be a cookbook as there is for ODEs. – Pcw. May 30 '15 at 15:58

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