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 03:38:41 -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?" Many thanks in advance, Aaron