Title

An elementary method for obtaining general solutions to systems of ordinary differential equations

Publication Name

Electronic Journal of Differential Equations

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, Liénard, van der Pol). The method relies only on a calculus background.

Open Access Status

This publication is not available as open access

Volume

2021

Article Number

58

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