Re: How to simplify?

• To: mathgroup at smc.vnet.net
• Subject: [mg96209] Re: How to simplify?
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Mon, 9 Feb 2009 05:35:51 -0500 (EST)
• References: <gmndih\$s09\$1@smc.vnet.net>

```Aaron,

BesselJ[0, r]

{{y[r] -> -1 + 1/2 r BesselJ[1, r] + C[2] + C[1] (
Log[r])}}

Apart from the constants C[2] and C[1] and the -1 this is exactly the
1/2 r BesselJ[1, r] you want to get. For a 2nd order diff eq the
constants look OK to me. I don't see what kind of numerical approach
(and why) you took with the results of DSolve to check the answer as
it is already in the correct form (taking C[2]=1 and C[1]=0).

What version of Mathematica are you using?

Cheers -- Sjoerd

On Feb 8, 9:59 pm, Aaron Fude <aaronf... at gmail.com> wrote:
> Hi,
>
> I'm sorry for totally belaboring this point, but I am having a hard
> time getting Mathematica be useful for me in this one respect. The
> following code shows that the linear ODE that I am trying to solve has
> 1/2 r BesselJ[1, r] as the particular solution. DSolve, however,
> returns an answer that I'm sure is correct. I tested it - numerically,
> the particular part is exactly 1/2 r BesselJ[1, r].
>
> But for someone who is looking for analytical insight, the answer is
> not useful. What can be done to simplify the expression so that it
> appears as 1/2 r BesselJ[1, r]
>
> S[r_] := 1/2 r BesselJ[1, r];
> D[S[r], {r, 2}] + 1/r D[S[r], r] + S[r] // FullSimplify
> DSolve[y''[r] + 1/r y'[r] + S[r] == BesselJ[0, r], y[r],
>   r] // FullSimplify
>
> I will gladly accept the answer "Nothing" and move on to looking for
> alternative solutions. Also note, this is just a model problem for me
> in preparation for more complicated ones. Last time I got several
> responses that said - "if you already know the solution to this
> problem, why are you trying to solve it?"
>