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

*To*: mathgroup at smc.vnet.net*Subject*: [mg93581] Re: DSolve and assuming: wrong solution found by Mathematica 6. A bug*From*: "sjoerd.c.devries at gmail.com" <sjoerd.c.devries at gmail.com>*Date*: Sun, 16 Nov 2008 07:03:07 -0500 (EST)*References*: <gf173i$idb$1@smc.vnet.net>

I'm not sure about this, but I don't think DSolve uses assumptions. The manual has the following about DSolve and symbolic parameters (tutorial/DSolveSymbolicAndInexactQuantities): In summary, the ability to solve differential equations with symbolic parameters is a powerful and essential feature of any symbolic solver such as DSolve. However, the following points should be noted. - The solution might be complicated, and such calculations often require significant time and memory. - The answer might not be valid for certain exceptional values of the parameters. - The solution might be easy to verify symbolically for some special values of the parameters, but in the general case a numerical verification method is preferable. Cheers -- Sjoerd On Nov 7, 1:00 pm, Pianiel <pdp... at gmail.com> wrote: > 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