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Re: not linear homogeneus differential equation system... too complicated for mathmeatica... maybe only for me! :)

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  • Subject: [mg41729] Re: [mg41718] not linear homogeneus differential equation system... too complicated for mathmeatica... maybe only for me! :)
  • From: Selwyn Hollis <selwynh at earthlink.net>
  • Date: Tue, 3 Jun 2003 07:13:11 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On Monday, June 2, 2003, at 04:35  AM, Alessandro wrote:

> For the type of system I'm studing I guess the system of differential
> equation (not liear) I'm going to asking about should have solution.
> Unfortunatly my knoledge about mathmatica is very poor, seems to be a 
> bit
> too complicated to try with paper and pencil in a reasoneble time, and 
> so
> I'd like to have some help.
> The Mathematica cell is:
>
>
> DSolve[
>     {     s'[t] == -A*s[t] +B*u[t],
>            u'[t] == A*s[t] - (E + C*a[t] + B)*u[t],
>            a'[t] == F*b[t] - C*a[t]*u[t],
>            b'[t] ==  C*a[t]*u[t] - (G + F)*b[t],
>            s[0] == s0, a[0] == a0, b[0] == 0,   u[0] == 0},
>     {s[t], u[t], a[t], b[t]}, t]
>
> I have two problem:
> 1) Before I was considering C=C' 1/a[t]... the system was linear and
> solvable. Nevertheless the solution was a very long formula. I needed 
> to
> compact the result with FullSimplify. Is it the right way or I can feed
> DSolve with some option in order to get a compact result by default?

DSolve followed by Simplify or FullSimplify is probably the right thing 
to do.

> 2)  Later I realized I was solving the erroneous equations. This new 
> non
> linear system is solved by Mathematica, after some minutes (CPU 2GHz 
> 512Mb),
> Mathematica answer with the same input I gave as output... well... I 
> think
> it is not able to solve it. There is some mathematica toolbox or some 
> way to
> solve it. It is probable I wiil need to change other things in the 
> equation
> so I'd prefer some suggestion in order to understand what to do 
> instead of
> the raw solution... however I will not disregard a solution :))))

You'll have to settle for a numerical solution using NDSolve. Of course 
this will require specific values for the coefficients.

-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis


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