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I try to solve a system of 16 linear differential equations, with a following code:

sminus = {{0, 0}, {1, 0}};
splus = {{0, 1}, {0, 0}};
kappa[t_, n_, d1_,g_] = {{xk[t, n, d1, g], yk[t, n, d1, g]}, {yk1[t, n, d1, g],zk[t, n, d1, g]}};
kappam[t_, n_, d1_,g_] = {{xkm[t, n, d1, g], ykm[t, n, d1, g]}, {ykm1[t, n, d1, g],zkm[t, n, d1, g]}};
kappamp[t_, n_, d1_,g_] = {{xkmp[t, n, d1, g], ykmp[t, n, d1, g]}, {ykmp1[t, n, d1, g],zkmp[t, n, d1, g]}};
kappapm[t_, n_, d1_,g_] = {{xkpm[t, n, d1, g], ykpm[t, n, d1, g]}, {ykpm1[t, n, d1, g],zkpm[t, n, d1, g]}}

DSolve[Flatten@{D[kappa[t, n, d1, g], t] == 
-n^2*(sminus.splus.kappa[t, n, d1, g] + 
       kappa[t, n, d1, g].sminus.splus) - (n + 
        1)^2*(splus.sminus.kappa[t, n, d1, g] + 
       kappa[t, n, d1, g].splus.sminus) + 
    2*n*(n + 1)*(splus.kappa[t, n, d1, g].sminus + 
       sminus.kappa[t, n, d1, g].splus
    - 
    2*n*(ConjugateTranspose[kappam[t, n, d1, g]].sminus + 
       splus.kappam[t, n, d1, g]) + 
    2*(n + 1)*(kappam[t, n, d1, g].splus + 
       sminus.ConjugateTranspose[kappam[t, n, d1, g]]) + 
    2*n*kappamp[t, n, d1, g] - 2*(n + 1)*kappapm[t, n, d1, g]) + 
 I*(sminus.splus.kappa[t, n, d1, g] - 
    kappa[t, n, d1, g].sminus.splus)*d1, 


D[kappam[t, n, d1, g], t] == 
   -n^2*(sminus.splus.kappam[t, n, d1, g] + 
           kappam[t, n, d1, g].sminus.splus) - (n + 
            1)^2*(splus.sminus.kappam[t, n, d1, g] + 
           kappam[t, n, d1, g].splus.sminus) + 
        2*n*(n + 1)*(splus.kappam[t, n, d1, g].sminus + 
           sminus.kappam[t, n, d1, g].splus)
        - n^2*kappam[t, n, d1, g] - (n + 1)^2*kappam[t, n, d1, g] + 
        2*((n + 1)^2*sminus.kappapm[t, n, d1, g] + 
           n^2*kappamp[t, n, d1, g].sminus - 
           n*(n + 1)*sminus.kappamp[t, n, d1, g] - 
           n*(n + 1)*kappapm[t, n, d1, g].sminus)
     + I*(sminus.splus.kappam[t, n, d1, g] - 
        kappam[t, n, d1, g].sminus.splus)*d1 - 
     I*d1*kappam[t, n, d1, g], 
   D[kappamp[t, n, d1, g], t] == 
    -n^2*(sminus.splus.kappamp[t, n, d1, g] + 
           kappamp[t, n, d1, g].sminus.splus) - (n + 
            1)^2*(splus.sminus.kappamp[t, n, d1, g] + 
           kappamp[t, n, d1, g].splus.sminus) + 
        2*n*(n + 1)*(splus.kappamp[t, n, d1, g].sminus + 
           sminus.kappamp[t, n, d1, g].splus)
        + 2*n*(n + 1)*kappapm[t, n, d1, g] - 
        2*n^2*kappamp[t, n, d1, g] + 
        2*((n + 1)^2*
            sminus.ConjugateTranspose[
              kappam[t, n, d1, g]] + (n + 1)^2*
            kappam[t, n, d1, g].splus - 
           n*(n + 1)*ConjugateTranspose[kappam[t, n, d1, g]].sminus - 
           n*(n + 1)*splus.kappam[t, n, d1, g])
     + I*(sminus.splus.kappamp[t, n, d1, g] - 
        kappamp[t, n, d1, g].sminus.splus)*d1, 
   D[kappapm[t, n, d1, g], t] == 
 -n^2*(sminus.splus.kappapm[t, n, d1, g] + 
           kappapm[t, n, d1, g].sminus.splus) - (n + 
            1)^2*(splus.sminus.kappapm[t, n, d1, g] + 
           kappapm[t, n, d1, g].splus.sminus) + 
        2*n*(n + 1)*(splus.kappapm[t, n, d1, g].sminus + 
           sminus.kappapm[t, n, d1, g].splus)
        + 2*n*(n + 1)*kappamp[t, n, d1, g] - 
        2*(n + 1)^2*kappapm[t, n, d1, g] + 
        2*(n^2*ConjugateTranspose[kappam[t, n, d1, g]].sminus + 
           n^2*splus.kappam[t, n, d1, g] - 
           n*(n + 1)*sminus.ConjugateTranspose[kappam[t, n, d1, g]] - 
           n*(n + 1)*kappam[t, n, d1, g].splus)
     + I*(sminus.splus.kappapm[t, n, d1, g] - 
        kappapm[t, n, d1, g].sminus.splus)*d1}, 
 Flatten@{kappa[t, n, d1, g], kappam[t, n, d1, g], 
   kappamp[t, n, d1, g], kappapm[t, n, d1, g]}, t]

Unfortunately Mathematica just instantly returns back the input without even attempting to solve it. It is not so relevant for me how long it would take to calculate the solution, but I would rather like to avoid to use NDSolve if it is possible.

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  • $\begingroup$ These are 16 equations with 16 variables. $\endgroup$ – Agnieszka May 25 '17 at 18:25
  • $\begingroup$ Notice your Flatten@yoursystem appears to do nothing and the result is still {mat1==mat2,mat3==mat4, mat5==mat6,mat7==mat8} which I assume you thought Flatten might turn into 16 individual equalities. I would be curious whether it might make any progress if you could get the 16 inequalities. The Conjugates in the equations also make me wonder whether they might be part of the sticking point. $\endgroup$ – Bill May 25 '17 at 19:14
  • $\begingroup$ Yes, I have used Flatten because of this example: link (I had the same error). Why it doesn't work here? $\endgroup$ – Agnieszka May 25 '17 at 20:06
  • $\begingroup$ Indeed, Mathematica seemed to have a problem with my ConjugateTranspose, I have added an equation for ConjugateTranspose[kappam], and now everything is working! Thanks! $\endgroup$ – Agnieszka May 26 '17 at 8:05

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