Abstract

OROZCO LOPEZ, Ronald. Analytical solution of the k-th order autonomous ordinary differential equation. Rev. Mat [online]. 2016, vol.23, n.1, pp.63-84. ISSN 1409-2433.

The main objective of this paper is to find the analytical solution of the autonomous equation y(k) = f (y) and prove its convergence using autonomous polynomials of order k, define here in addition of the formula of Faá di Bruno for composition of functions and Bell polynomials. Autonomous polynomials of order k are defined in terms of the boundary values of the equation. Also special values of autonomous polynomials of order 1 are given.

Keywords : Autonomous equation; Bell polynomials; Autonomous polynomials.

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