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Need Help: 1st order nonlinear differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg51215] Need Help: 1st order nonlinear differential equation
• From: Wolfgang_Eggert at gmx.de (Wolfgang)
• Date: Fri, 8 Oct 2004 02:55:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I need to solve the following 1st order nonlinear differential
equation. I am really stuck. DSolve refuses to give an answer and I
need an algebraic solution.

Derivative[1][a][Z] == 
  -((1/n + ((r*(n - 1))/(n^2*a[Z]))*((1 - a[Z])*n - (¦Ñ + 2*¦Ä)*Z))/
    (r*(n - 1)*((n*(r - 1) - 2*r)/(n^2*a[Z]^2))*Z*((1 - a[Z])*n -
¦Ä*Z)))

where

\!\({0 ¡Ü a ¡Ü 1, Z ¡Ý 0, n > 2, 1 > ¦Ä > 0, 1 > ¦Ñ > 0, 1 > r > 
    0, 0 < r < n\/\(n - 2\)}\)

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.)?

Maybe I am thinking slow but I am really in trouble.

Any help is greatly appreciated. Thank you for your time.

Respectfully;
Wolfgang

• Follow-Ups:
  • Re: Need Help: 1st order nonlinear differential equation
    • From: DrBob <drbob@bigfoot.com>