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