Replacement rule for a function and its derivative

Question

I have this equation:

  EOM1 = Subscript[x1, t, t] + ω1^2*x1 /. 
    Subscript[x1_, m__] :> D[x1[x, t], m] /. 
      x1 -> x1[x, t]

The problem with the rule is that it doubles the argument. How can I avoid writing the arguments [x,t] twice.

Thanks

Answer 1

Please try this:

 EOM1 = Subscript[x1, t, t] + \[Omega]1^2*x1[x, t] /. 
   Subscript[x1_, m__] :> D[x1[x, t], m] /. x1 -> x1[x, t] /. x1[x, t] -> x1

Answer 2

I am not sure I understand your meaning, but if write

EOM1 = Subscript[x1, t, t] + ω1^2*x1 /. 
Subscript[x1_, m__] :> D[x1[x, t], m] /. 
  x1 -> x1

you obtain

x1 \[Omega]1^2+(x1^(0,2))[x,t]