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

Journal Article


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, Liénard, van der Pol). The method relies only on a calculus background.

Publication Date


  • 2021

Citation


  • Rodrigo, M. R. (2021). An elementary method for obtaining general solutions to systems of ordinary differential equations. Electronic Journal of Differential Equations, 2021.

Scopus Eid


  • 2-s2.0-85115750063

Web Of Science Accession Number


Volume


  • 2021

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, Liénard, van der Pol). The method relies only on a calculus background.

Publication Date


  • 2021

Citation


  • Rodrigo, M. R. (2021). An elementary method for obtaining general solutions to systems of ordinary differential equations. Electronic Journal of Differential Equations, 2021.

Scopus Eid


  • 2-s2.0-85115750063

Web Of Science Accession Number


Volume


  • 2021