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arXiv · 2012.14021

Solution of the system of two coupled first-order ODEs with second-degree polynomial right-hand sides

Francesco Calogero·Farrin Payandeh
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Abstract

The explicit solution of the initial-values problem is exhibited of a subclass of the autonomous system of 2 coupled first-order ODE s with second-degree polynomial right-hand sides, hence featuring 12 a prior arbitrary (time-independent) coefficients. The solution is explicitly provided if the 12 coefficients are expressed by explicitly provided formulas in terms of 10 a prior arbitrary parameters; the inverse problem to express these 10 parameters in terms of the 12 coefficients is also explicitly solved, but it is found to imply as it were, a posterior that the 12 coefficients must then satisfy 4 algebraic constraints, which are explicitly exhibited.Special sub cases are also identified the general solutions of which are completely periodic with a period independent of the initial data, or are characterized by additional restrictions on the coefficients which identify particularly interesting models.

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Francesco Calogero, Farrin Payandeh. 2020-12-27. Solution of the system of two coupled first-order ODEs with second-degree polynomial right-hand sides. https://doi.org/10.1007/s11040-021-09400-7

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