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Solution of a non-linear ODE

• To: mathgroup at smc.vnet.net
• Subject: [mg81890] Solution of a non-linear ODE
• From: sigmundv at gmail.com
• Date: Sat, 6 Oct 2007 04:33:09 -0400 (EDT)

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