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  1. {x''[t] + x[t] == 0, x[-t] == x[t]} /. x -> ( Cos[#] & )
  2. (*True,True *)
  3.  
  4. DSolve[{x''[t] + x[t] == 0, x[-t] == x[t]}, x, t]
  5. (*DSolve[{x''[t] + x[t] == 0, x[-t] == x[t]}, x, t]*)
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