A Method to Tackle First Order Ordinary Differential Equations with Liouvillian Functions in the Solution

We present an algorithm to solve First Order Ordinary Differential Equations (FOODEs) extending the Prelle-Singer (PS) Method. The usual PS-approach miss many FOODEs presenting Liouvillian functions in the solution (LFOODEs). We point out why and propose an algorithm to solve a large class of these previously unsolved LFOODEs. Although our algorithm does not cover all the LFOODEs, it is an elegant extension mantaining the semi-decision nature of the usual PS-Method. Universidade do Estado do Rio de Janeiro, Instituto de F́ısica, Departamento de F́ısica Teórica, R. São Francisco Xavier, 524, Maracanã, CEP 20550–013, Rio de Janeiro, RJ, Brazil. E-mail: [email protected] idem. E-mail: [email protected] idem. E-mail: [email protected] 1