On Explicit Structure of Solution Space of a Class of the First Order Nonlinear Ordinary Differential Equation

Abstract:

      In this paper, the concept of the canonical integrable equation is introduced. A criterion is given involving the n+1 coefficient of a given equation ｗ′＝∑sum from ｉ＝０ to n ａ_ｉ（ｚ）ｗ^ｉ（ｚ） that the solution space of the equation has an explicit structure. According to this criterion, it can be judged that the solution space of this class of nonlinear differential equiation has an explicit or implicit strctrure, therefore, an analytic qualitative analyese can be made on it. Moreover, this criterion can be used to d...