高阶非线性常微分方程组的可积类型

Integrable Types of Nonlinear Ordinary DifferentialEquation Sets of Higher 0rders

线性微分方程在物理学，力学及控制论中有着广泛应用，近年来在国内外一些重要刊物上发表多篇有关求微分方程精确解的论文。本文在这些论文的基础上，借助于Ｌｃｉｂｎｉｚ求导公式及变换组法，进而提出了高阶非线性常微分方程组的求解法，于是论证了它的可积性，所得结果是相应文献结果的推广。

Because of the extensive applications of nonlinear ordinary differential equa-tion in physics,mechanics and cybernetics,there have been many papers on the exact solution to differential equation in some major publications both at home and abroad in recent years. Based on these papers and in virtue of Leibniz for-mula, and transformation sets technique, this paper puts forth the solution to nonlinear ordinary differential equation set of higher-orders; moreover,its inte-grability is proven. The results abtained are the generalization of those in the references.