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)

```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.