Symmetry Lie algebras and properties of linear ordinary differential equations with maximal dimension

Abstract

Solutions of linear iterative equations and expressions for these solutions in terms of the parameters of the first-order source equation are obtained. Based on certain properties of iterative equations, finding the solutions is reduced to finding solutions of the second-order source equation. We have therefore found classes of solutions to the source equations by letting the parameters of the source equation be functions of a specific type such as monomials, functions of exponential and logarithmic type.