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Re: Mathematica and Mathieu DEQ Results?

• To: mathgroup at smc.vnet.net
• Subject: [mg91180] Re: [mg91134] Mathematica and Mathieu DEQ Results?
• From: DrMajorBob <drmajorbob at att.net>
• Date: Fri, 8 Aug 2008 07:16:36 -0400 (EDT)
• References: <7958044.1218126462486.JavaMail.root@m08>
• Reply-to: drmajorbob at longhorns.com

Surely your input wasn't

DSolve[x''[t] + (4[Pi]^2 - 2((-Pi^2/5) Cos[2 (Pi t)/100])))x[t] == 0,
x[t], t]

since it (a) has an unmatched right parenthesis and (b) involves the  
(nonexistent) function 4 applied to Pi, 4[Pi].

Paste in the actual input, and we might get started.

Bobby

On Thu, 07 Aug 2008 03:39:05 -0500, amzoti <amzoti at gmail.com> wrote:

> Hi All,
>
> 1. I am using Mathematica, to solve the following DEQ:
> DSolve[x''[t] + (4[Pi]^2 - 2((-Pi^2/5) Cos[2 (Pi t)/100])))x[t] == 0,
> x[t], t] (1)
>
>  This results in a solution of even and odd Mathieu functions as
> follows:
>
>  x[t] = C[1] MathieuC[40000, -2000, Pi*t/100] + C[2] MathieuS[40000,
>  -2000, Pi*t/100]
>
>  2. However, according to <http://mathworld.wolfram.com/
> MathieuDifferentialEquation.html,
>  the result is:
>
>  x[t] = C[1] MathieuC[4 Pi ^2, -Pi^2/5, Pi*t/100] + C[2] MathieuS[4 Pi
>  ^2, -Pi^2/5, Pi*t/100] (2)
>
>  a. I am confused why I am getting these totally different results.
>
>  b. The paper I am reading <epsppd.epfl.ch/Roma/pdf/P2_091.pdf shows
>  three different plots that match with (2) - where I am able to
>  duplicate the results/plots of the paper exactly using this method.
>
>  Can someone out there shed light on why this is the case?
>
>  Why can't Mathematica get the same result (or is it that the DEQ does
> not have a unique solution based on some properties of Mathieu
> functions)?
>
>  Any insights are appreciated!
>
>  ~A
>
>



-- 
DrMajorBob at longhorns.com