Electron. J. Differential Equations, Vol. 2021 (2021), No. 58, pp. 120.
An elementary method for obtaining general solutions to systems of
ordinary differential equations
Marianito R. Rodrigo
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
firstorder 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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