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MathGroup Archive 1998

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Boundary cond. at Infinity



I neet to solve diff. equation:

DSolve[
  {
    y''[x]-a^2 y[x]==Sinh[x]/Cosh[x]^2,
    y[0]==0, y[Infinity]==0
  },y[x],x
]

Math 3.0 complains about boundary condition at "Infinity". Well, I then
solve it with boundary cond. at zero only :

DSolve[
  {
    y''[x]-a^2 y[x]==Sinh[x]/Cosh[x]^2,
    y[0]==0
  },y[x],x
]

And Math.3.0 give me an answer in terms of PolyGamma's and
Hypergeometric2F1's with one constant C[2] which I want to find by
myself. To find it I need to know the behavior of e.g.
Hypergeometric2F1[(1 + a)/2, 1, 1 + (1 + a)/2, -E^(2*x)] at infinity.
How can I ask Mathematica to show me the behavior of arbitrary function
at infinity? I expect to get something like x*Exp[-2*x] i.e. Taylor is
of no use in this case since the behavior is exponential with unknown
power.

Your help will be appeciated very much. Send a copy of reply by email as
well. Thanx



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