       2 coupled diff. eqns

• To: mathgroup at smc.vnet.net
• Subject: [mg21078] 2 coupled diff. eqns
• From: Henk Jansen <hj at rdr-nl.com>
• Date: Sun, 12 Dec 1999 23:51:45 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```I have the following set of two coupled differential equations:

c f
f' = a -  ----------------
___________
\  /  2    2
\/  f  + g

c g
g' = b -  ----------------
___________
\  /  2    2
\/  f  + g

where a, b and c are constants. Trying to solve this system (if
possible), after typing

DSolve[
{D[f[t], t] == a - (w f[t])/(Sqrt[f[t]^2 + g[t]^2])\),
D[g[t], t] == b - (w g[t])/(Sqrt[f[t]^2 + g[t]^2])\)
},
{f[t], g[t]},
t]

Mathematica returns with the following message:

"Part::partw: Part 2 of g'[f] does not exist."

without solution. I have two questions:

1. Does anyone know how to interprete this message?

2. If the system is not solvable, is there a clever coordinate
transformation for which the system can be solved?

Thanks,

Henk Jansen

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