Re: Can't solve Diff Equ
- To: mathgroup at smc.vnet.net
- Subject: [mg42753] Re: Can't solve Diff Equ
- From: "Kevin J. McCann" <KevinMcCann!kjm at uunet.uu.net>
- Date: Fri, 25 Jul 2003 05:07:59 -0400 (EDT)
- References: <bfo4ca$cbk$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I assume that the "x" is the same on both sides of the equation. You should
use the modified version
equ=D[x[t], {t, 2}] == D[c[x[t]], {x[t], 1}] D[x[t], {t, 1}]
so that the time dependence is apparent on both sides. Now
DSolve[equ,x[t],t]
gives (it looks better in normal form)
{{x[t] -> InverseFunction[
Integrate[1/(c[K$29] +
C[1]), {K$29, K$30,
#1}] & ][t + C[2]]}}
Kevin
"Oliver Friedrich" <oliver.friedrich at tzm.de> wrote in message
news:bfo4ca$cbk$1 at smc.vnet.net...
> 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
>