Please follow the following book

Differential equations and synamical systems by lawrence perko //

paguirre.mat.utfsm.cl/edo-2015-2/perko.pdf

The place where I usually check for this is this one http://eqworld.ipmnet.ru/en/solutions/basbooks.htm

If you have mathematica software and a very good computer try this

imax=2;

X=Table[x[i][t],{i,imax}]

K=Table[k[i,j],{i,imax},{j,imax}]

eq=Table[x[i]'[t]==x[i][t]*\!\(

\*UnderoverscriptBox[\(\[Sum]\), \(j = 1\), \(imax\)]\(k[i, j]*\(x[j]\)[t]\)\),{i,imax}]

DSolve[eq,X,t]

imax is the dimension

Dear Aditya Kuchibhotla,

The system you want to integrate is an n-dimensional quadratic system, close also to Lottka-Volterra equations. Even if n=2 you cannot expect to integrate it. Only some particular systems can be integrated in an explicit form. Accoring to Pitchaimani M information above, general classification of 2-dimensional system is due to Lyagina [19] on Perko's list of additional references. More recently John REYN published the monograph: PHASE PORTRAITS of PLANAR QUADRATIC SYSTEMS.

Mathematics and Its Applications (Springer), 583. Springer, New York, 2007 in which, I guess, you find his contribution to general classification of planar quadratic system.

Best regards,

Piotr Grabowski