DSolve:: Bessel's differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg64261] DSolve:: Bessel's differential equation
- From: bd satish <bdsatish at gmail.com>
- Date: Wed, 8 Feb 2006 03:53:58 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
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)?