Symmetry and transformation properties of iterative ordinary differential equation

Symmetries of linear iterative equations and new conditions on the infinitesimals are obtained. Regarding the expressions of the solutions in terms of the parameters of the source equation, an ansatz is made on the original parameters. We have also obtained an expression for the source parameters of the transformed equation under equivalence transformations. We conducted this work with a special emphasis on second-, third- and fourth-order equations, although some of our results are valid for equations of a general order.