Re: Eliminating unknown functions from partial differential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg41083] Re: Eliminating unknown functions from partial differential equations
- From: bobhanlon at aol.com (Bob Hanlon)
- Date: Thu, 1 May 2003 05:00:21 -0400 (EDT)
- References: <b8o1b0$ov2$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
eqn = {x'[t]==y[t], y'[t]==-x[t]};
Reduce[Join[eqn,D[#,t]& /@ eqn], x[t], NestList[D[#,t]&, y[t], 2]]
-Derivative[2][x][t] == x[t]
DSolve[%, x[t],t]
{{x[t] -> C[1]*Cos[t] + C[2]*Sin[t]}}
However, this can be done directly
DSolve[eqn, {x[t],y[t]},t]
{{x[t] -> C[1]*Cos[t] + C[2]*Sin[t],
y[t] -> C[2]*Cos[t] - C[1]*Sin[t]}}
Bob Hanlon
In article <b8o1b0$ov2$1 at smc.vnet.net>, Stepan Yakovenko <yakovenko at ngs.ru>
wrote:
<< Is it possible to eliminate some of unknown functions from a partial
differential equation ?
For instance :
x'[t]=y[t]
y'[t]=-x[t]
->
x''[t]=-x[t]
>><BR><BR>