Path: csiph.com!v102.xanadu-bbs.net!xanadu-bbs.net!feeder.erje.net!eu.feeder.erje.net!news.swapon.de!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail
From: Axel Vogt <&noreply@axelvogt.de>
Newsgroups: comp.soft-sys.math.maple
Subject: Re: Bessel And Airy Functions in Solutions
Followup-To: sci.math.symbolic
Date: Fri, 04 Apr 2014 11:53:13 +0200
Lines: 36
Message-ID: <bq7dooFfun2U1@mid.individual.net>
References: <x6udnZIbHKrEr6POnZ2dnUVZ_tadnZ2d@megapath.net>
Reply-To: &noreply@axelvogt.de
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
X-Trace: individual.net Z6nMQ5l0VqZD9oEEshFI0gwPk9vf+rMoTuP0nNIl/DqpcEzp4=
Cancel-Lock: sha1:Bm4Sjz+qA4DLhuA0z6NNkG2QJZ0=
User-Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:24.0) Gecko/20100101 Thunderbird/24.4.0
In-Reply-To: <x6udnZIbHKrEr6POnZ2dnUVZ_tadnZ2d@megapath.net>
Xref: csiph.com comp.soft-sys.math.maple:870

On 04.04.2014 06:17, Thomas D. Dean wrote:
> I have a problem,
>
> ode:=diff(y(x),x,x)+(a*x+b)*y(x)=0;
> raw_soln:=dsolve(ode);
> soln1:=convert(raw_soln,BesselI);
>
> This gives an expression with several terms.
>
> Maxima gives a solution,
>
> [y = bessel_y(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*%k2*sqrt(a*x+b)
>            +bessel_j(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*%k1*sqrt(a*x+b)]
> where bessel_y is the second kind and bessel_j is the first kind.
>
> If I assume %k2 is _C2 and %k1 is _C1
>
> maxima := y(x) = BesselY(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*_C2*sqrt(a*x+b)
>      +BesselJ(1/3,2*(a*x+b)^(3/2)/(3*abs(a)))*_C1*sqrt(a*x+b);
> soln2:=convert(maxima,BesselI);
>
> I am having problems determining if these are the same.
>
> Ideas?
>
> Tom Dean

Better use different constants for Maxima's solution. And convert
to Airy functions. Then comparing the inputs for the Airy functions
show different expressions. May be you need 0 < a to get the 'same'
as your raw_solution

   convert(maxima, Airy):
   collect(%, [AiryAi, AiryBi]):
   simplify(%, size);
   maxima2:=%;