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)?
|
|