How to eliminate a variable from coupled ODEs?


I found this question with an answer: How to eliminate variables in ODE?

With[{f = Function[t, {x'[t] + x[t]/10 + y[t], x[t] - y'[t] + z[t], x[t] + 3 y[t] - z'[t]}]},  With[{ndiff = Function[{exp, t}, Array[D[exp, {t, #}] &, Length[f[t]] + 1, 0]]}, Eliminate[Join @@  ndiff[f[t], t] == 0, Complement[ndiff[f[t], t] // Variables, ndiff[x[t], t]]]]] 

I want to know why is this Array[D[exp, {t, #}] &, Length[f[t]] + 1, 0] created? If I change the Length of the array the solution returns ‘True’.