Francesco Calogero ; Farrin Payandeh - Explicitly solvable systems of two autonomous first-order Ordinary Differential Equations with homogeneous quadratic right-hand sides

ocnmp:7336 - Open Communications in Nonlinear Mathematical Physics, May 20, 2021, Volume 1 - https://doi.org/10.46298/ocnmp.7336
Explicitly solvable systems of two autonomous first-order Ordinary Differential Equations with homogeneous quadratic right-hand sides

Authors: Francesco Calogero ; Farrin Payandeh

After tersely reviewing the various meanings that can be given to the property of a system of nonlinear ODEs to be solvable, we identify a special case of the system of two first-order ODEs with homogeneous quadratic right-hand sides which is explicitly solvable. It is identified by 2 explicit algebraic constraints on the 6 a priori arbitrary parameters that characterize this system. Simple extensions of this model to cases with nonhomogeneous quadratic right-hand sides are also identified, including isochronous cases.


Volume: Volume 1
Published on: May 20, 2021
Accepted on: May 15, 2021
Submitted on: April 8, 2021
Keywords: Mathematics - Dynamical Systems


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