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MathGroup Archive 2005

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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


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