       Re: Non linear diff eq

• To: mathgroup at smc.vnet.net
• Subject: [mg15578] Re: [mg15491] Non linear diff eq
• From: jtischer at col2.telecom.com.co (Cl-Jurgen Tischer)
• Date: Tue, 26 Jan 1999 13:44:53 -0500 (EST)
• References: <199901180922.EAA20789@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

```Francisco,
I'm afraid this is not a problem to be solved with Mathematica, but with
some easy arguments. Of course Mathematica is of help to find the
answer, but only to the extent you don't know elementary functions and
elementary DE's.
So solve the equation for x positive and for x negative (use
Mathematica), both solutions can not oscillate fast at zero, so you
have two cases, the function going up or down in zero. If going up, the
function is of the form c Sin[t] with positive c, so a has to be
positive and equal to c Sin, If going down, the function has to be
of the type c Sinh[t] with c negative, so a has to be negative and
equal to c (E-1/E).

Jurgen

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, x==a.
>
> How can I work it out with Mathematica?
>
> thanks!
>
> Francisco Gutierrez
>

```

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