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Re: DSolve:: Bessel's differential equation
 To: mathgroup at smc.vnet.net
 Subject: [mg64267] Re: DSolve:: Bessel's differential equation
 From: "JensPeer Kuska" <kuska at informatik.unileipzig.de>
 Date: Wed, 8 Feb 2006 06:29:50 0500 (EST)
 Organization: Uni Leipzig
 References: <dsccr4$pb1$1@smc.vnet.net>
 Sender: ownerwrimathgroup at wolfram.com
Hi,
my Mathematica 5.2 return
{{y[x] > (Sqrt[2*L + 2*x]*BesselI[0,
2*Sqrt[k^2*(L + x)]]*C[1])/Sqrt[2*L  2*x] +
(Sqrt[2*L + 2*x]*BesselK[0, 2*Sqrt[k^2*(L +
x)]]*
C[2])/Sqrt[2*L  2*x]}}
Regards
Jens
"bd satish" <bdsatish at gmail.com> schrieb im
Newsbeitrag news:dsccr4$pb1$1 at smc.vnet.net...

 Hi buddies,

 Here is a differential equation ,
which could not be done by
 DSolve (in Version 5.0 ).
 This occurs in the mathematical modelling of a
simple pendulum of length L
 and a parameter k .
 (Actually , k ^ 2 = frequency of oscillation^2 /
acceleration due to gravity
 )

 (L  x) y''[x]  y'[x] + k^2 y[x] ==
0 .... (1)

 The above equation is in fact reducible to
Bessel's differential equation
 (with order n = 0 )

 with the substituions Lx = z and s = 2 k
Sqrt[z]

 y''[s] + 1 /s y'[s] + y[s] ==0
.... (2)

 The textbook says that the solution of eqn (1)
contains a BesselJ[0,2 k
 Sqrt[Lx] ].


 How can I get DSolve to answer (1) directly ,
without resorting to eqn (2)?


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