       Re: How to simplify?

• To: mathgroup at smc.vnet.net
• Subject: [mg96216] Re: How to simplify?
• From: dh <dh at metrohm.com>
• Date: Mon, 9 Feb 2009 05:37:07 -0500 (EST)
• References: <gmndih\$s09\$1@smc.vnet.net>

```
Hi Aaron,

verion 7 of mma gives:

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

Daniel

Aaron Fude 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?"

>

>

> Aaron

>

```

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