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Arbitrary functions _Fs

Posted on 2010-02-08 15:07 By Mehtab (3)
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I want to solve the following PDE with boundary conditions, but unfortunately I do not know the meaning of _F1 and _F2 in this stuation. Would you please help me to find these arbitrary functions?

> PDE := diff(U(y, z), y, y)+diff(U(y, z), z, z) = 0;

> with(PDEtools);

> sol := pdsolve(PDE);
                    U(y, z) = _F1(z - I y) + _F2(z + I y)

What's the meaning of _F1 and _F2 in this situation? How can I find them? It's an urgent situation. Please help me as soon as possible.

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edgar's picture

"arbitrary functions" may be

Comment on 2010-02-10 07:03 from edgar (Maple Rating 3 267)

"arbitrary functions" may be annoying. But take ANY two functions, then this formula will give you a solution of the PDE.
Your PDE "Laplace's equation" has many volumes devoted to it. So probably the user will need to do some study before he can get Maple to produce a useful answer of a particular boundary value problem.
---
G A Edgar

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