       How to simplify?

• To: mathgroup at smc.vnet.net
• Subject: [mg96161] How to simplify?
• From: Aaron Fude <aaronfude at gmail.com>
• Date: Sat, 7 Feb 2009 03:52:32 -0500 (EST)

```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?"