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[2] + C[1] 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?" > > Many thanks in advance, > > Aaron >