       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))/C) -2 E^((g rho (x +
C))/C) lambda)/ (2 E^((g rho (x + C))/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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