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MathGroup Archive 2006

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Re: DSolve:: Bessel's differential equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64279] Re: DSolve:: Bessel's differential equation
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 9 Feb 2006 02:44:45 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <dsccr4$pb1$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup 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  L-x = z and s = 2 k 
Sqrt[z]
|
|             y''[s] + 1 /s  y'[s] + y[s] ==0 
.... (2)
|
| The text-book says that the solution of eqn (1) 
contains a BesselJ[0,2 k
| Sqrt[L-x] ].
|
|
|  How can I get DSolve to answer (1) directly , 
without resorting to eqn (2)?
|
| 



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