常系数线性微分方程解法研究的新认识  

New method of understanding constant coefficient linear differential equation

作　　者：赵临龙 ZHAO Lin-long(School of Mathematics and Statistics,Ankang University,Ankang 725000,P.R.C.)

机构地区：[1]安康学院数学与统计学院,陕西安康725000

出　　处：《西南民族大学学报（自然科学版）》2019年第2期200-205,共6页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：高等学校大学数学教学研究与发展中心项目(CMC20170401);陕西省精品资源共享课程建设项目(2015-73);安康学院教育教学成果奖培育项目(2018A-02)

摘　　要：对于常系数线性微分方程L(x)=f(t),通过变换将其化为常系数线性微分方程组x'=Ax+f(t).分别就常系数线性微分方程的特征根为单根和重根情况,探求函数f(t)构成的可积条件,并对于可解的常系数线性微分方程给出其解,对于不可解的常系数线性微分方程进行讨论.For linear differential equations with constantcoefficients L(x)=f(t), the system oflinear differential equations with constant coefficients is transformed into asystem of linear differential equations with constant coefficients x′=Ax+f(t). In the case that thecharacteristic root of linear differential equation with constant coefficientsis single root and double root, the integrable condition of function f(t) is obtained, and the solution of solvablelinear differential equation with constant coefficient is given. The unsolvable linear differential equationswith constant coefficients are discussed.

关 键 词：常微分方程组 一阶线性微分方程 代数线性方程 特征根 行向量 

分 类 号：O175.1[理学—数学]