Birational Transformations on Algebraic Ordinary Differential Equations
Sprache des Titels:
We describe a group of birational transformations acting on the set of algebraic ordinary differential equations (AODEs) of arbitrary order n. This transformation group, by its action, partitions the set of algebraic ODEs into equivalence classes. All the elements in a given equivalence class exhibit the same behavior in terms of rational solvability. For a big family of algebraic ODEs we show how to decide whether the given equation can be transformed into an equivalent autonomous ODE.