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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



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