A note on internality of certain differential systems

Abstract We prove two results, generalizing certain theorems by Jin and Moosa (2020, Trans. Amer. Math. Soc. , 373, 4863–4887), on the internality of the system of differential equations $$ \begin{align*} \begin{cases} \begin{aligned} x' &= f(x)\ y' &= g(x)y,\ \end{aligned} \end{cases} \end{align*} $$ where f and g are rational functions in one variable.