The general solution of an ordinary differential equation

Abstract

We consider in this paper an implicit non-linear ordinary differential equation P(Z, y, y’) = O. There are several types of solutions. The singular solutions are characterized by the fact they make & vanish. No such characterization of the so called general solution can be found in classical treatises. We propose here an algorithmic method to compute a similar characterisation of the general solution. We apply the result to give some insight on the local behaviour of the solutions in the neighbourhood of a singular solution.

Locations

• CiteSeer X (The Pennsylvania State University) - View - PDF