On Expansion of a Solution of General Non-autonomous Polynomial Differential Equation

Abstract

We give a recursive formula for an expansion of a solution of a general non-autonomous polynomial differential equation. The formula is given on the algebraic level with a use of shuffle product. This approach minimizes the number of integrations on each order of expansion. Using combinatorics of trees we estimate the radius of convergence of the expansion.

13 pages, To be published in Journal of Dynamical and Control Systems

References in corpus (2)

• Integrability of Lie systems through Riccati equations
• A geometric approach to integrability conditions for Riccati equations