DSolve Bessels

• To: mathgroup at smc.vnet.net
• Subject: [mg19045] DSolve Bessels
• From: "Alberto Verga" <verga at marius.univ-mrs.fr>
• Date: Thu, 5 Aug 1999 01:34:39 -0400
• Organization: Universite de la Mediterranee Aix en Provence
• Sender: owner-wri-mathgroup at wolfram.com

```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 Phénomènes Hors Equilibre.
12, av. Général Leclerc, 13003 Marseille, France.
Tel: 33 (0) 4 91 64 44 76 - Fax 33 (0) 4 91 08 16 37

```

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