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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.

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