Re: I have an operator, How do I DSolve it?

• To: mathgroup at smc.vnet.net
• Subject: [mg96202] Re: I have an operator, How do I DSolve it?
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Mon, 9 Feb 2009 05:34:34 -0500 (EST)
• References: <gmndhs\$s04\$1@smc.vnet.net>

Hi,

I'm not sure to understand your question, because

B[m_, f_] := (D[f[#], {#, 2}] +
1/# D[f[#], {#, 1}] + (1 - m^2/#^2) f[#]) &

does already what you want. If you don't like to have
the Function[{r},__] and prefer a Slot[] argument

G[m_, f_] :=
Block[{r},
DSolve[B[m, f][r] == 0, f, r][[1]] /.
Function[{r}, expr_] :> Function @@ {expr /. r -> Slot[1]}]

Regards
Jens

Aaron Fude 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.
>