多项式微分方程的基本定理(续)

FUNDAMENTAL THEOREM OF POLYNOMIAL ORDINARY DIFFERENTIAL EQUATION

常微分方程与代数方程有同类的发展历史 ,即经过实域到复域 ,从定量到定性。但前者比后者更困难。后者以高斯的“代数方程的基本定理”作为结束。前者则以系统的研究开始于秦元勋的《常微分方程定义的积分曲面》 ,1985 )西北大学出版社。本文给出这方面的三个基本定理 ,得到平行于高斯定理的多项式常微分方程的通解法式。

Ordinary Differential Equation and Algebraic Equation have similar history of development,namely from real domain to complex domain,from analytic to qualitative,but the former is much more difficult than the latter.The latter is concluded by Gauss's famous “Fundamental Theorem of Algebra”.The former started from Qin's book《Integral Surfaces defined by Ordinary Differential Equation》(1985)Northwest University Press,Xian,PRC.This article contains three fundamental theorems in this respect,ended with the fundamental theorem of normal general solution of polynomial ordinary solution.English version was published in Qin's Collected Works (1994) Beijing Education Science Press,but not sold on the market.