Re: Challenging ODE

In article <1113985879.710163.154130@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<john_ramsden@xxxxxxxxxxxxxx> wrote:
>
>Anyone care to have a crack at solving the following
>ODE, or try running it through Mathematica:

> dy/dx = m.(1 + y^2 - x^2) (m constant)

Maple says:

2
2 _C1 WhittakerW(m/4 + 1, 1/4, m x )
y(x) = ------------------------------------
x m (_C1 %2 + %1)

2
(3 + m) WhittakerM(m/4 + 1, 1/4, m x )
- 1/2 --------------------------------------
x m (_C1 %2 + %1)

2 2
(-_C1 + 2 _C1 x m - _C1 m) %2 + (-1 + 2 m x - m) %1
- 1/2 -----------------------------------------------------
x m (_C1 %2 + %1)

2
%1 := WhittakerM(m/4, 1/4, m x )

2
%2 := WhittakerW(m/4, 1/4, m x )



Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

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