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 > > Sent via Deja.com http://www.deja.com/ Before you buy.