2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70769We consider simply generated trees and study multiplicative functions on rooted plane trees. We show that the associated generating functions satisfy differential equations or difference equations. Our approach considers B-series from Butcher's theory, the generating functions are seen as generalized Runge-Kutta methods19 pages, 1 figureCombinatoricsProbability05a15;05c05;30b10;46154;81s25text