       Re: Simplifying a second order eq. system

• To: mathgroup at smc.vnet.net
• Subject: [mg45969] Re: Simplifying a second order eq. system
• From: "T.Telliskivi" <maria.08.6689847 at telia.com>
• Date: Sat, 31 Jan 2004 05:20:31 -0500 (EST)
• References: <bvd7jv\$51v\$1@smc.vnet.net>
• Reply-to: "T.Telliskivi" <maria.08.6689847 at telia.com>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Gunnar,
I cannot give you a solution but:
1: use u[x,t], i[x,t] and are you sure to use Dt instead of D ?
myEqn1 = -D[u[x,t],x] == r i[x,t] + l D[i[x,t],t]
myEqn2 = -D[i[x,t],x] == s u[x,t] + c D[u[x,t],t]
2: about: <<In := Solve[{myEqn1,myEqn2}, {Dt[u,{x,2}]}]>>
Dt[u,{x,2} = D[my Eqn1,x] ???

Tanel

"Gunnar Lindenblatt" <Gunnar.Lindenblatt at pobox.com> skrev i meddelandet
news:bvd7jv\$51v\$1 at smc.vnet.net...
> Hi,
>
> I just switched from another system to Mathematica
> 5. While all "complicated" operations (like importing Wave-Files,
filtering,
> parameter fitting, plotting) just work fine, I still have problems with
the
> "basics" like solving or even simplifying equations:
>
> For example, to get the telegraph equation by self-induction and
capacitive
> coupling:
>
> (One can solve this problem on the space of a postage stamp...)
>
> In := Remove["Global`*"]
>
> In := myEqn1 = -Dt[u,x] == r i + l Dt[i,t]
>
> In := myEqn2 = -Dt[i,x] == s u + c Dt[u,t]
>
>
>
> Direct approach: Using "Solve"
>
> In := Solve[{myEqn1,myEqn2}, {Dt[u,{x,2}]}]
>
> results an empty set of solutions:
>
> {{}}
>
>
>
> Second try: Using "Reduce"
>
> In := Reduce[{myEqn1,myEqn2}, {Dt[u,{x,2}]}]
>
> results:
>
> Reduce::nsmet: This system cannot be solved with the methods available to
> Reduce.
>
> Third try: Using "Eliminate"
>
> In := Eliminate[{myEqn1,myEqn2}, {Dt[i,x],Dt[i,t]}]
>
> results:
>
> True
>
> That's fine! However, it does not really help me...
>
>
>
> (By the way, the result should be:
>
> Dt[u,{x,2}]== r s u + (r c + l s) Dt[u,t] + l c Dt[u,{t,2}])
>
> Any ideas? -- Perhaps this problem is too simple for Mathematica, so it
> rejects any help ;-)
>
> - Gunnar
>
>
>
>
> --
> Gunnar Lindenblatt
> e-mail: Gunnar.Lindenblatt at pobox.com
>
>

```

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