Re: How to simplify?
- To: mathgroup at smc.vnet.net
- Subject: [mg96218] Re: How to simplify?
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Mon, 9 Feb 2009 05:37:29 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <gmndih$s09$1@smc.vnet.net>
In article <gmndih$s09$1 at smc.vnet.net>, Aaron Fude <aaronfude at gmail.com> wrote: > I'm sorry for totally belaboring this point, but I am having a hard > time getting Mathematica be useful for me in this one respect. The > following code shows that the linear ODE that I am trying to solve has > 1/2 r BesselJ[1, r] as the particular solution. DSolve, however, > returns an answer that I'm sure is correct. I tested it - numerically, > the particular part is exactly 1/2 r BesselJ[1, r]. > > But for someone who is looking for analytical insight, the answer is > not useful. What can be done to simplify the expression so that it > appears as 1/2 r BesselJ[1, r] > > > S[r_] := 1/2 r BesselJ[1, r]; > D[S[r], {r, 2}] + 1/r D[S[r], r] + S[r] // FullSimplify > DSolve[y''[r] + 1/r y'[r] + S[r] == BesselJ[0, r], y[r], > r] // FullSimplify [snip] What output did you get on your system, which is...? Here is what I get on mine: In[1]:= S[r_] := 1/2 r BesselJ[1, r]; D[S[r], {r, 2}] + 1/r D[S[r], r] + S[r] // FullSimplify DSolve[y''[r] + 1/r y'[r] + S[r] == BesselJ[0, r], y[r], r] // FullSimplify Out[2]= BesselJ[0, r] Out[3]= {{y[r] -> -1 + 1/2 r BesselJ[1, r] + C[2] + C[1] Log[r]}} In[4]:= {$Version, $ReleaseNumber} Out[4]= {"6.0 for Mac OS X x86 (64-bit) (May 21, 2008)", 3} Regards, --Jean-Marc