Re: Re: nonlinear differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg54771] Re: [mg54725] Re: nonlinear differential equation
- From: DrBob <drbob at bigfoot.com>
- Date: Tue, 1 Mar 2005 01:58:27 -0500 (EST)
- References: <cvhequ$qft$1@smc.vnet.net> <200502250618.BAA02402@smc.vnet.net> <cvrqae$p3s$1@smc.vnet.net> <200502280827.DAA11437@smc.vnet.net>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
> As you can see, the conditions s[0]==0 and s'[0]==v0 hold only if v0==0.
Because:
Off[Solve::verif, Solve::tdep]
deqn = s''[t] - a*s[t]^2 - b*s[t] - c == 0;
ddeqn =
((Integrate[#1, t] &) /@
Expand[Derivative[1][s][t]*
#1] &) /@ deqn;
Block[{t = 0, s}, s[0] = 0; ddeqn]
(1/2)*Derivative[1][s][0]^2 == 0
Bobby
On Mon, 28 Feb 2005 03:27:13 -0500 (EST), Peter Pein <petsie at arcor.de> wrote:
> DrBob wrote:
>
>> Yikes!!! Good luck inverting the functions involved.
>>
>> Off[Solve::verif, Solve::tdep]
>> deqn = Derivative[2][s][t] -
>> a*s[t]^2 - b*s[t] - c == 0;
>> ddeqn =
>> ((Integrate[#1, t] & ) /@
>> Expand[Derivative[1][s][t]*
>> #1] & ) /@ deqn
>> s /. DSolve[{%}, s, t]
>> (-c)*s[t] - (1/2)*b*s[t]^2 -
>> (1/3)*a*s[t]^3 +
>> (1/2)*Derivative[1][s][t]^
>> 2 == 0
> ...
>
> As you can see, the conditions s[0]==0 and s'[0]==v0 hold only if v0==0.
>
--
DrBob at bigfoot.com
www.eclecticdreams.net