Explicitly solvable systems of two autonomous first-order Ordinary Differential Equations with homogeneous quadratic right-hand sides

Abstract

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.

18 pages

References in corpus (2)

• New algebraically solvable systems of two autonomous first-order ordinary differential equations with purely quadratic right-hand sides
• Solution of the system of two coupled first-order ODEs with second-degree polynomial right-hand sides