An elementary method for obtaining general solutions to systems of ordinary differential equations
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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.
CitationRodrigo, M. R. (2021). An elementary method for obtaining general solutions to systems of ordinary differential equations. Electronic Journal of Differential Equations, 2021(58), pp. 1-20.
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