Electron. J. Differential Equations, Vol. 2021 (2021), No. 58, pp. 1-20.

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

Marianito R. Rodrigo

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.

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Marianito R. Rodrigo
School of Mathematics and Applied Statistics
University of Wollongong
Wollongong, New South Wales, 2422, Australia
email: marianito_rodrigo@uow.edu.au

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