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DSolve and assuming: wrong solution found by Mathematica 6. A bug or

• To: mathgroup at smc.vnet.net
• Subject: [mg93425] DSolve and assuming: wrong solution found by Mathematica 6. A bug or
• From: Pianiel <pdpdel at gmail.com>
• Date: Fri, 7 Nov 2008 06:01:31 -0500 (EST)

Hi all,

I tried unsuccessfully to find the solution of a differential equation
using Mathematica 6.0.2.1. The given solution is wrong. Would it be
possible to help me?  Here is what I have done:

Knowing that n is an integer, I want to solve the following
differential equation:

DSolve[r^2A''[r]+r A'[r]+(K^2r^2-n^2)A[r]==r( n B1- B2),A[r],r]

So what I wrote is:

Res=Assuming[Element[n,Integers],DSolve[r^2A''[r]+r A'[r]+(K^2r^2-
n^2)A[r]==r( n B1- B2),A[r],r]]

I checked using:

Res /. n -> 1

And the result is Indeterminate! Sad!! (same thing with n->2 or n-
>3, ...)

On the contrary when I change directly the value of n in the equation
and set it n=1:

DSolve[r^2 A''[r] + r A'[r] + (K^2 r^2 - 1^2) A[r] == r ( 1 B1 - B2),
A[r], r]

Mathematica find a solution!
Where is the bug? How to find the general solution with n integer
for:

DSolve[r^2A''[r]+r A'[r]+(K^2r^2-n^2)A[r]==r( n B1- B2),A[r],r]

Is Mathematica able to do that??

Thanks somuch for your help!

Pianiel