2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135275The aim of the present paper is to propose an algorithm for a new ODE--solver which should improve the abilities of current solvers to handle second order differential equations. The paper provides also a theoretical result revealing the relationship between the change of coordinates, that maps the generic equation to a given target equation, and the symmetry $\D$-groupoid of this target.Symbolic ComputationI.1.2text