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 MathieuC[40000, -2000, Pi*t/100] + C MathieuS[40000, > -2000, Pi*t/100] > > 2. However, according to <http://mathworld.wolfram.com/ > MathieuDifferentialEquation.html, > the result is: > > x[t] = C MathieuC[4 Pi ^2, -Pi^2/5, Pi*t/100] + C 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