Re: DSolve:: Bessel's differential equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg64267] Re: DSolve:: Bessel's differential equation*From*: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>*Date*: Wed, 8 Feb 2006 06:29:50 -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)? | |