Re: Non linear diff eq

• To: mathgroup at smc.vnet.net
• Subject: [mg15569] Re: Non linear diff eq
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Tue, 26 Jan 1999 13:44:47 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <78077s\$ag7\$3@dragonfly.wolfram.com>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Fancisco,

you will not find  a closed. You can't solve the equation numerical
because the numerical solvers require that the  right hand side has
smooth derivatives. But You can come  closer to the solution with

deqn=x''[t]+Abs[x[t]]==0;
deqn1= (Expand[x'[t]*#] & /@ deqn) /.  a_+b_==0 :> a==-b;

deqn2=Integrate[Expand[#],{t,0,tau}] & /@
deqn1  /.HoldPattern[Integrate[Abs[x_[t_]]*x_'[t_],{t_,a_,b_}]] :>

Dot[{1,-1},(x[t]^2*Sign[x[t]] /. {{t->b},{t->a}}) ]

deqn3=Solve[deqn2 /. tau->t /. x[0]->0,x'[t]]/. Rule -> Equal//Flatten

Now it is up to you (because only you know if a> 0 or a<0) to solve the
two equations.

Hope that helps
Jens

Fancisco Gutierrez wrote:
>
> Hi! I have the following nonlinear diff. eq.:  x'' + Abs[x]=0, t element
> of [0,1], with these boundary conditions: x[0]==0, x[1]==a.
>
> How can I work it out with Mathematica?
>
> thanks!
>
> Francisco Gutierrez

```

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