       Re: Surprising DSolve problem

• To: mathgroup at smc.vnet.net
• Subject: [mg123971] Re: Surprising DSolve problem
• From: "Brandon D. Batista" <bdbatista at gmail.com>
• Date: Tue, 3 Jan 2012 05:27:00 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201020742.CAA09063@smc.vnet.net>

```Hi Sam,

I reviewed this case, and using Mathematica 8.0.4 was able to replicate
your lack of solution results for the case involving the inclusion of
constants.  I also tried to use Mathematica 7.0.1 as well as Mathematica
5.2, and the same lack of results occurred.  However, using another CAS I
was able to obtain the following result to the differential equation, which
follows (it is somewhat complicated):

y(x) = C1*Sqrt[(Cosh[2x/a] - 1)/(Cosh[2x/a] + 1)] + C2*((Cosh[2x/a] -
1)*(Log[Cosh[2x/a] + Sqrt[Cosh[2x/a]^2 - 1]]) - 2*Sqrt[Cosh[2x/a]^2 -
1])/Sqrt[Cosh[2x/a]^2 - 1]

where 'C1' and 'C2' are constants, 'Sqrt' is the square root, and 'Log' is
the natural logarithm.

Hopefully this information helps.

Best,
B. Batista

On Mon, Jan 2, 2012 at 02:42, Sam Takoy <sam.takoy at yahoo.com> wrote:

> Hi,
>
> I find that my Mathematica (8.0.1)
>
> can do
>
> DSolve[ y''[x] + (2 y[x])/(Cosh[x]^2) == 0, y, x]
>
> but can't do
>
> DSolve[ y''[x] + (2 y[x])/(a^2 Cosh[x/a]^2) == 0, y, x] (*Additional
> constant "a")
>
> If I am not mistaken, the equations are equivalent by a trivial change
> of variables.
>
> What's going on here?
>
> Thanks,
>
> Sam
>
>

```

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