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DSolve & Cosh
*To*: mathgroup at smc.vnet.net
*Subject*: [mg6194] DSolve & Cosh
*From*: dwarf at wam.umd.edu (Dwarf)
*Date*: Thu, 27 Feb 1997 02:53:32 -0500
*Organization*: University of Maryland, College Park, MD
*Sender*: owner-wri-mathgroup at wolfram.com
Hello all,
I am trying to solve the hanging chain problem using Mathematica
(Student Ver 2.2 -- I don't have Win 95 or a Mac to be able to use 3.0)
and getting Mma to solve the resulting ODE is giving me fits! I know the
solution is neatly expressed in terms of Cosh, but instead I get some
monstrous (but equivalent) expression in terms of exponentials.
Is anyone aware of a function package which will convert exponentials to
hyperbolic sines & cosines? Something like ComplexToTrig, perhaps? I can
demonstrate thet the two answers are equivalent, but I had hoped for
something more direct.
Here is the ODE, for those who care:
C y'[x]==Sqrt[(lambda+rho g y[x])^2-C^2]
and the answer (in terms of Cosh)
Y[x_]:=(C Cosh[rho g x/C+C2]-lambda)/(rho g)
and the answer I get from Mma (which requires the use of Calculus`DSolve`)
{{y[x] -> (C^2 + E^((2 g rho (x + C[1]))/C) -2 E^((g rho (x +
C[1]))/C) lambda)/ (2 E^((g rho (x + C[1]))/C) g rho)}}
Any help would be appreciated. . .
+----------------------------+
| | Good things come in small packages,
| Greg Anderson | but big things don't, unless they're
| dwarf at wam.umd.edu | inflatable or require some assembly.
| timbwolf at eng.umd.edu |
| | -- The Tick
+----------------------------+
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