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
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