Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 58, pp. 1-20.

Title: An elementary method for obtaining general solutions to systems of 
       ordinary differential equations
       
Author: Marianito R. Rodrigo (Univ. of Wollongong,  New South Wales, Australia)

Abstract: 
 An analytical method is proposed for finding the general solution of a system of ordinary
 differential equations (ODEs). The general solution is expressed as a series which in
 some cases can be summed to give an expression in closed form. A sufficient condition
 for the series to converge is derived. Illustrative examples are given for scalar
 first-order ODEs (Riccati, Abel, homogeneous, Bernoulli, linear, separable) and for
 higher order ODEs (Airy, linear oscillator, Lienard, van der Pol).
 The method relies only on a calculus background.

Submitted March 17, 2021. Published June 26, 2021.
Math Subject Classifications: 34A05, 34A25, 34A34.
Key Words: Ordinary differential equation; general solution; analytical method;
           exact solution.