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)?