Re: I have an operator, How do I DSolve it?
- To: mathgroup at smc.vnet.net
- Subject: [mg96223] Re: [mg96159] I have an operator, How do I DSolve it?
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 9 Feb 2009 05:38:25 -0500 (EST)
- Reply-to: hanlonr at cox.net
B[m_, f_] := (D[f[#], {#, 2}] +
1/# D[f[#], {#, 1}] + (1 - m^2/#^2) f[#]) &
DSolve[B[m, S][r] == 0, S[r], r][[1]]
{S[r] -> C[1]*BesselJ[m, r] + C[2]*BesselY[m, r]}
Bob Hanlon
---- Aaron Fude <aaronfude at gmail.com> wrote:
=============
Hi,
I have defined a differential operator, but what's the syntax for
using it in DSolve?
I have the Bessel operator
B[m_, f_] := (D[f[#], {#, 2}] +
1/# D[f[#], {#, 1}] + (1 - m^2/#^2) f[#]) &
It's the Bessel operator for now, but I will soon replace it with a
different one. This is for testing puposes only.
Now, how do I use it in DSolve?
So far I use
DSolve[S''[r] + 1/r S'[r] + (1 - m^2/r^2) S[r] == 0, S[r], r]
but that's not a good solution because I have to different expressions
for the same thing. I want to used B only.
Many thanks in advance,
Aaron