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MathGroup Archive 2005

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Re: nonlinear differential equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54725] Re: nonlinear differential equation
  • From: Peter Pein <petsie at arcor.de>
  • Date: Mon, 28 Feb 2005 03:27:13 -0500 (EST)
  • References: <cvhequ$qft$1@smc.vnet.net> <200502250618.BAA02402@smc.vnet.net> <cvrqae$p3s$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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.

-- 
Peter Pein
Berlin


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