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Here is a set of first-order differential coupled equations with

eqns = {x1'[
     t] == (x4[t]^4 + (x4[t]^2 + x5[t]^2)^2 - x6[t]^4 + 
      x6[t]^2 x1[t] + x1[t]^2 + x3[t]^2 - x1[t] (x4[t]^2 + x5[t]^2)),
   x2'[t] == (x2[t]^2 + x3[t]^2),
   x3'[t] == x3[t]^2 (x1[t] + x3[t] - x4[t]^2 - x5[t]^2 + x6[t]^2),
   x4'[t] == x4[t]^3,
   x5'[t] == -x5[t]^3,
   x6'[t] == x6[t] (x6[t]^2 - x4[t]^2 - x5[t]^2 - x7[t]^3), 
   x7'[t] == -x7[t]^3};
DSolve[eqns, {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t], x7[t]}, t]

Mathematica returns an empty solution. Can anyone suggest a possible solution to it?

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    $\begingroup$ You have a complicated, non-linear coupled system of 7 differential equations. There is very likely no analytic solution. Where did you get this system from? You can use NDSolve to get numeric solution. $\endgroup$
    – Domen
    Commented Jun 10 at 12:58
  • $\begingroup$ DSolve cannot even solve eqns[[{1,3}]] for {x1, x2} with the other dependent variables in those two equations set to 1, so it is very unlikely that it can solve the entire set. Note however that DSolve[eqns[[{4, 5, 6, 7}]], {x4, x5, x6, x7}, t] does return a solution. $\endgroup$
    – bbgodfrey
    Commented Jun 10 at 17:46
  • $\begingroup$ @Nasser: Excuse me, why have removed your answer? I have not even copied it. Could you please rewrite it. Txs $\endgroup$
    – SciJewel
    Commented Jun 11 at 7:10

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