2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57049We present a method for reducing the order of ordinary differential equations satisfying a given scaling relation (Majorana scale-invariant equations). We also develop a variant of this method, aimed to reduce the degree of non-linearity of the lower-order equation. Some applications of these methods are carried out and, in particular, we show that second-order Emden-Fowler equations can be transformed into first-order Abel equations. The work presented here is a generalization of a method used by Majorana in order to solve the Thomas-Fermi equation.RevTex, 8 pagesMathematical PhysicsHigh Energy Physics - PhenomenologyHigh Energy Physics - TheoryClassical Analysis and ODEsGeneral Mathematics34A25; 34A05; 34A34; 34B30; 85A04text