Re: Solution for a System of ODEs and equations
- To: mathgroup@smc.vnet.net
- Subject: [mg12595] Re: [mg12560] Solution for a System of ODEs and equations
- From: Wouter Meeussen <eu000949@pophost.eunet.be>
- Date: Mon, 25 May 1998 14:25:06 -0400
At 18:11 23-05-98 -0400, Vivek Pai wrote:
>Please help if possible:
>
>I have the following problem :
>
>I need to Solve two ordinary differential equations combined with a
>trancedental equation for eg :
>
>dx/dt = f(x,y); (1)
>dy/dt = m g(x,y); (2)
>
>and
>
>m Log(m) = xy; (3)
>
>
>In other words I do not have an explicit expression for 'm' to be
>introduced into equation 2.
>
>Can Mathematica help me with a simple 3 or 4 line code.
>
>Regards
>
>
>
dear Vivek,
your line (3) *can* be written as a explicit function for m:
Solve[m Log[m]==x[t] y[t],m]
gives
{{m -> x[t] y[t] /ProductLog[ x[t] y[t] ]}}
So, you want :
soln=
DSolve[{
D[u[t], t] == f[u[t], v[t]],
D[v[t], t] == g[u[t], v[t]] u[t] v[t]/ProductLog[u[t] v[t]]
},
{u[t], v[t]}, t]
This set of coupled differential equations is still mulling after 5
minutes, so I'll just abort it now.
I hope you have more luck & patience with it.
wouter.
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc@vandemoortele.be
eu000949@pophost.eunet.be