       Re: 2 coupled diff. eqns

• To: mathgroup at smc.vnet.net
• Subject: [mg21175] Re: 2 coupled diff. eqns
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 17 Dec 1999 01:22:59 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <831vap\$g58@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Henk,

the system appears to be not solvable. You can try it in polar
coordinates with

deqn = {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])}

deqn1 = FullSimplify[
Solve[Simplify[
deqn /. Flatten[{#, D[#, t]} & /@ {f[t] -> r[t]*Sin[phi[t]],
g[t] -> r[t]*Cos[phi[t]]}],
Element[r[t], Reals] && r[t] >= 0], {r'[t], phi'[t]}]]

and

DSolve[Flatten[deqn1 /. Rule -> Equal] , {r[t], phi[t]}, t]

But the best seems to make some assuptions on r[t] and phi[t] to get
some limit cases.

Hope that helps
Jens

Henk Jansen wrote:
>
> 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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