Re: Coupled Differential Equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg34814] Re: Coupled Differential Equations*From*: shubi at nusun.jinr.ru (Nodar Shubitidze)*Date*: Sat, 8 Jun 2002 05:21:24 -0400 (EDT)*References*: <adkf9d$9u8$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"Cyrill Slezak" <Cyrill.Slezak at Physik.Uni-Augsburg.DE> wrote in message news:<adkf9d$9u8$1 at smc.vnet.net>... > I understand that NDSolve will solve a set of first order coupled. diff.eqn. > Here is my problem: I have a set of 20+ equation that all have the exact > same structure and I can't seem to find an easy way to input them. For any > help I'd be highly appreciative. The equations are of the form > > d V_k(l)/d l = V_k(l) + Sum[ V_k'(l), (k not equal k')] > > where k is the number of diff. eqn. > > Thanks for any help, > > Cyrill Hello, You may write your system as: d V_k(x) /d x = Sum[ V_m(x),{m=1,nmax}] Then d V_1(x)/d x =d V_2(x)/d x =d V_3(x)/d x = . . . and V_2(x) = V_1(x) + C_2 V_3(x) = V_1(x) + C_3 . . . substitute to equation we receive: V_1(x) = C_1 * Exp[ n*x ] -(C_2 + C_3 + ... + C_nmax) / nmax with previos equals it is a general solution. Nodar Shubitidze