Re: Solution of a non-linear ODE

*To*: mathgroup at smc.vnet.net*Subject*: [mg81936] Re: Solution of a non-linear ODE*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sun, 7 Oct 2007 05:29:43 -0400 (EDT)*References*: <fe7hgc$ok8$1@smc.vnet.net>

Hi, your second equation is not very helpful because FullSimplify @@ odesys gives you a single second order equation for the two variables u[t] and v[t] and you need a second second order equation for v[t]. You can try deq3 = FullSimplify @@ odesys; odesys1 = {deq3, D[#, t] & /@ eq2} and DSolve[ odesys1, {u[t], v[t]}, t] Regards Jens sigmundv at gmail.com wrote: > Distinguished group members, > > I would like you to try the following: > > First define > > f[u_, v_] := 1 > eq1 = D[ArcTan[v'[t]/u'[t]], t] + 1/2 (D[Log[f[u[t], v[t]]], u[t]] > v'[t]^2 - D[Log[f[u[t], v[t]]], v[t]] u'[t]) == 0; > eq2 = u'[t]^2 + v'[t]^2 == 1/f[u[t], v[t]]; > odesys = {eq1, eq2}; > ic = {u[0] == 0, v[0] == 0, u'[0] == 0, v'[0] == 1}; > > Then try to solve 'odesys', with the initial conditions 'ic', either > using DSolve or NDSolve, or both. What do you get? For NDSolve I get > the warning > > Solve::svars: Equations may not give solutions for all "solve" \ > variables. > > and the the input is returned unevaluated. > > When I use NDSolve on the initial value problem, the system runs > several minutes, without returning any result. > > Can any of you explain this behaviour? > > When doing the same calculations with another similar software > package, I get solutions easily. Therefore it seems strange that > Mathematica does not return any solution. > > Best regards, > Sigmund Vestergaard > >