Re: question about ODE
- To: mathgroup at smc.vnet.net
- Subject: [mg117870] Re: question about ODE
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Sat, 2 Apr 2011 02:42:32 -0500 (EST)
You don't need NIntegrate, since:
Integrate[Sin[x'[t]*L], {L, 0, 1}]
(1 - Cos[Derivative[1][x][t]])/Derivative[1][x][t]
and
Integrate[Sin[x'[t]*L], L]
-(Cos[L Derivative[1][x][t]]/Derivative[1][x][t])
But there may be a problem with the conditions:
Clear[x]
DSolve[{x''[t] == -Integrate[Sin[x'[t]*L], {L, 0, 1}], x[0] == 0,
x'[0] == 10}, x, t]
{}
DSolve::bvfail : "For some branches of the general solution, unable
to solve the conditions. >>"
The same thing happens with
DSolve[{x''[t] == -((1 - Cos[Derivative[1][x][t]])/
Derivative[1][x][t]), x[0] == 0, x'[0] == 10}, x, t]
Symbolic solution looks difficult, but perhaps you can provide limits
and change the last version to NDSolve.
Bobby
On Fri, 01 Apr 2011 02:34:06 -0500,
<alexey_timohin at mail.ru> wrote:
>
> Hello Everybody! Please help me to find answer on this question
>
> How can I solve this ODE
>
> x''[t]=-NIntegrate[Sin[x'[t]*L], {L,0,1}] , x[0]=0, x'[0]=10
>
> The integral in this ODE must be evalueted in each step of solving ODE. But I don't know how can I realise it.
--
DrMajorBob at yahoo.com