Re: question

*To*: mathgroup at smc.vnet.net*Subject*: [mg26480] Re: question*From*: Alexandra Milik <amilik1 at compuserve.com>*Date*: Thu, 28 Dec 2000 02:52:20 -0500 (EST)*References*: <91sbtt$8kk@smc.vnet.net> <91ujih$ahf@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

The equation has a first integral, it is 1/(u'+1) + Log[1+u'] + u^2/2= C were C is the integration constant. So you can try DSolve as well. Also you can check the NDSolve solution using this formula. Alex "Kevin J. McCann" schrieb: > The wise words of Abraham Boyarsky on 21 Dec 2000 02:36:29 -0500: > > > I believe the following is a Liouville differential equation: > > > > u"[x] + u[x](u'[x] +1)^2 = 0 > > > > on [0,1]. > > > > How does one solve it? > > > > > This is a nonlinear DE. I would use NDSolve with IC u[0]==1,u'[0]==0 and > with u[0]==0,u'[0]==1. > > Kevin