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Re: Need Help: 1st order nonlinear differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg51362] Re: Need Help: 1st order nonlinear differential equation
• From: Wolfgang_Eggert at gmx.de (Wolfgang)
• Date: Fri, 15 Oct 2004 02:46:19 -0400 (EDT)
• References: <8bakj17y4gzj@legacy>, <8h978wy7ulns@legacy>
• Sender: owner-wri-mathgroup at wolfram.com

Sorry, after I solved the problems with the format of the posting I
became aware that there is a typo in the restriction. This should
read:

1 >= a >= 0 && n > 2 && Z >= 0 && 1 > \[Delta] > 0 && 1 > \[Rho] > 0
&& 0 < r < n/(-2 + n)

Please ignore the term 1 > r > 0 in the previous posting. It creates
inconsistencies. Moreover, please consider Z>=0 instead of Z>0.

It was very early in the morning when I prepared the original message
to get help. Please excuse the shortcomings in the posting, there is
no other typo left.


On 12 Oct 04 04:27:46 -0400 (EDT), Wolfgang wrote:
>I became aware that the essential lines in my previous posting are
>unreadable. So let me correct for this. My problem is:
>
>I need to solve the following 1st order nonlinear differential
>equation. I am really stuck. DSolve refuses to give an answer and I
>need the algebraic solution for a[Z].
>
>
>Derivative[1][a][Z] == (a[Z]*((-1 + n)*r* (n - Z*(2*\[Delta] +
>\[Rho])) + n*(1 + r - n*r)*a[Z]))/ ((-1 + n)*(n*(-1 + r) -
>2*r)*r*Z*(-n + Z*\[Delta] + n*a[Z]))
>
>where
>
>1 >= a >= 0 && n > 2 && Z > 0 && 1 > \[Delta] > 0 && 1 > \[Rho] > 0
&&
>1 > r > 0 && 0 < r < n/(-2 + n)
>
>
>Does anybody know how to solve this problem?
>
>Has anybody tips how to impose domain restrictions while solving
>differential equations in
>Mathematica (version 5.0.1.0.)?
>
>
>Any help is greatly appreciated. Thank you for your time.
>
>
>Respectfully;
>Wolfgang