Say I have an expression of this sort:


and so on...

I would like to ask Mathematica to neglext all expressions having derivatives higher than a given order (say N).

What would be a good solution for that?

Derivative[5][x1][t] + Derivative[3][x2][t] + x1[t] + 
  Derivative[2][x1][t] /. Derivative[k_][x_][t_] /; k >= 3 :> 0

x1[t] + (x1^[Prime][Prime])[t]

For understanding /; see the documentation of Condition.

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