Jordan标准型在非齐线性常微分方程中的应用  

Application of Jordan Canonical Form to Nonhomogeneous Linear Ordinary Differential Equations

作　　者：徐千里[1] 徐水清 

机构地区：[1]湖南城市学院数学与计算科学系 [2]湖南益阳市资阳区国基试验学校,湖南益阳413049

出　　处：《湖南城市学院学报（自然科学版）》2006年第3期34-36,共3页Journal of Hunan City University:Natural Science

摘　　要：利用等价方程组,Jordan标准型与常数变易公式,研究了一类n阶常系数非齐线性常微分方程P(D)y=a(x)coseλx+b(x)sineμx,得到了它的一种新的求解方法.最后给出了一个详细的实例.In this paper, the nth order nonhomogeneous linear ordinary differential equations with constant coefficints P（D）y=a（x）cose^λx＋b（x）sine^μx , Where P（D） = D^n ＋a1D^n-1 ＋...＋an-1D＋an is differential polynomial operator, a1, a2,..., an, A and μ are arbitrary constants, a（x） and b（x） are continuous functions and it is investigated by using equivalent system, Jordan canonical form and variation of constants formula. A new method of finding its solution is obtained. Finally, an illustrative example is presented in detail.

关 键 词：非齐线性常微分方程 等价方程组 基解矩阵 标准型 常数变易公式 

分 类 号：O175.1[理学—数学]