Re: Open Form ODE?

• To: mathgroup at smc.vnet.net
• Subject: [mg23851] Re: Open Form ODE?
• From: Brian Higgins <bghiggins at ucdavis.edu>
• Date: Mon, 12 Jun 2000 01:17:42 -0400 (EDT)
• References: <8hsul7\$di1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```David,

Mathematica is able to find an analytical solution to your ode using
DSolve:

DSolve[{6x'[t]^2 - 2x[t]x''[t] - \[Lambda] x[t]^4 == 0, x[0] == 1, x'[0] ==
0},x,t]

The solution is

{x -> (Sqrt[2]/Sqrt[2 + #1^2*\[Lambda]] & )}

This is the same solution that NDSolve finds numerically, and is
the Blue plot  on your web site. Obviously for positive \[Lambda],
the solution remains bounded for all time. If there is a singular
solution to the ODE (cf Clairaut eqn.), then DSolve is unable to find
it (at least with the current form).
Hope this helps,

Cheers,
Brian

In article <8hsul7\$di1 at smc.vnet.net>,
"David" <rcq at antispam.msgto.com> wrote:
> Hi,
>
> Please see this web site for a non-linear ODE problem.
>
> http://members.tripod.com/ivylee123
>
> This example could not be solved by another system.
> What does Mathematica do with it analytically and numerically?
>
> Does it have an exact solution, which can be used to verify the
numerical
> solution?
>
> Where is there a list of open form ODE problems which have
numerical
> solutions posted using different numerical methods?
>
> Thanks
>
>

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