Problem regarding to solve "6 nonlinear dynamic system of first order differential equation" analytically ( approximated )

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I have some problem to solve, Problem is regarding to solve "6 nonlinear dynamic system of first order differential equation" analytically ( approximated answer):-

1) Can I solve this system of equation by using Perturbation technique, if possible can you suggest some example or article where more than 3 system of equation is solved.

2) If any other approximated technique

Diffrential equations