An elementary method for obtaining general solutions to systems of ordinary differential equations
Date
2021-06-26
Authors
Rodrigo, Marianito R.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Ordinary differential equation, General solution, Analytical method, Exact solution
Citation
Rodrigo, M. R. (2021). An elementary method for obtaining general solutions to systems of ordinary differential equations. <i>Electronic Journal of Differential Equations, 2021</i>(58), pp. 1-20.
Rights
Attribution 4.0 International