Re: Can't solve Diff Equ
- To: mathgroup at smc.vnet.net
- Subject: [mg42806] Re: Can't solve Diff Equ
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 30 Jul 2003 04:07:32 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <bfo4ca$cbk$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
DSolve[D[x[t], {t, 2}] == D[c[x[t]], {x[t], 1}] D[x[t], {t, 1}], x[t],
t]
gives
{{x[t] -> InverseFunction[Integrate[(c[K$52] + C[1])^(-1),
{K$52, K$53, #1}] & ][t + C[2]]}}
but nobody know what c[] is.
Regards
Jens
Oliver Friedrich wrote:
>
> Hallo,
>
> I try to solve the following differential equation:
>
> equ=D[x[t], {t, 2}] == D[c[x], {x, 1}] D[x[t], {t, 1}]
>
> DSolve[equ,x[t],t]
>
> Mathematica 4.2 returns it unsolved.
>
> 1. Does DSolve need any more information ?
>
> 2. What kind of DiffEqu is it, can't solve DSolve those kinds at all ?
>
> 3. Are there some special packages capable of "cracking" this equation ?
>
> To give some background information.
>
> An acoustic signal propagates through a medium with propagation velocity
> c[x], propagation depends on the location in the medium. I'm searching
> for a function x[t] which describes the location of the pulse as a
> function of time.
>
> Any ideas ? I guess, that this problem should be well known. Is this
> equation a well known one in this area?
>
> Oliver Friedrich