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In this paper,we investigate the classification of higher order algebraic ordinary differential equations (AODEs) with respect to (w.r.t.) their rational solvability.More precisely,we find a group of ane linear transformations,such that a given higher order AODE can be transformed to a more easier solvable AODE by the action on the given AODE of an element in this group,and some certain characteristics,e.g.associated system,can be preserved during this transformation process.