On certain solvable systems of 4 nonlinear Ordinary Differential Equations

Some interesting (periodic!) solutions of certain systems of $4$ nonlinear Ordinary Differential Equations $dx_{n}\left( t\right) /dt=P_{2}^{\left( n\right) }\left[ x_{m}\left( t\right) \right] /\left[ x_{1}\left( t\right) +x_{2}\left( t\right) \right] ,~n,m=1,2,3,4~$, where $P_{2}^{\left( n\right) }\left[ x_{m}\left( t\right) \right]$ are $4$ polynomials of degree $2$ in the $4$ dependent variables $x_{m}\left( t\right)$, are obtained.