Solution of linear and slightly nonlinear differential equations

2 Joseph Liouville, Memoires sur le developpement des fonctions ou parties defonctions en siries dontles divers termes sont assujettis d satisfaire d une mime Equation diff&rentielle du second ordre, contenant un parametre variable, J. de Math., 2, 16-35, 418-436 (1837).t The meaning of "slightly" depends on the goodness of results expected from the process.Beyond that we shall not attempt to define it.