Re: DSolve Bessels

• To: mathgroup at smc.vnet.net
• Subject: [mg19154] Re: DSolve Bessels
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 5 Aug 1999 23:58:56 -0400
• Organization: Universitaet Leipzig
• References: <7ob7ld\$348@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Alberto,

it is always wise to read the manual, in Mathematica 3.0 as well
as in 4.0

FunctionExpand[D[yy, {x, 2}] + D[yy, x]/x + (1 - 1/x^2)yy]

give 0

FullSimplify[] (what call FunctionExpand[]) will work as well.

Regards
Jens

Alberto Verga wrote:
>
> Mathematica 3 seems to be not able to show that J_1(x) is solution of
> the Bessel equation:
>
> in: yy=BesselJ[1,x]
>
> in: Simplify[D[yy,{x,2}]+D[yy,x]/x+(1-1/x^2)yy]
>
> out: 1/(4x^2) (x^2 BesselJ[-1, x] + 2 x BesselJ[0, x] - 4 BesselJ[1, x]
> +
>       2 x^2 BesselJ[1, x] - 2 x BesselJ[2, x] + x^2 BesselJ[3, x])
>
> Using trivial transformations one gets 0, Mathematica does it not.
> One obtains the correct answer (out: 0) in other systems.
>
> Is Mathematica 4 able to show that a solution obtained with DSolve, when
> replaced back into the original equation, is actually the solution?
>
> in: DSolve[D[y[x],{x,2}]+D[y[x],x]/x+(1-1/x^2)y[x]==0,y[x],x]
> out: y[x] ->BesselJ[1, Sqrt[x^2]] C[1] +...
> --
> Alberto Verga - verga at marius.univ-mrs.fr
> Institut de Recherche sur les Phnomnes Hors Equilibre.
> 12, av. General Leclerc, 13003 Marseille, France.
> Tel: 33 (0) 4 91 64 44 76 - Fax 33 (0) 4 91 08 16 37

```

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