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.

Comment: 18 pages

• 34A05 - Explicit solutions, first integrals of ordinary differential equations
• 34A34 - Nonlinear ordinary differential equations and systems