一类变系数齐次线性微分方程组的解法  

Solution of a Class of Homogeneous Linear Differential Equations with Variable Coefficients

作　　者：赵舵舵 韩欣欣 肖一凡 Zhao Duoduo;Han Xinxin;Xiao Yifan(Chizhou University,Chizhou 247000,China)

机构地区：[1]池州学院,安徽池州247000

出　　处：《黑河学院学报》2023年第6期182-185,共4页Journal of Heihe University

基　　金：安徽省教育厅教研一般项目“探析高等数学课程思政体系的构建策略”(2020jyxm1291);安徽省教育厅微分方程及其应用教学团队“常微分方程”(2020XSZTD02);池州学院重点科研项目“一类双调和方程的解的存在性研究”(CZ2018ZRZ05);池州学院重点科研项目“基于事件触发的半马尔科夫跳变多智能体系统一致性研究”(CZ2023ZRZ04)。

摘　　要：常系数微分方程可以很容易地用许多方法来处理,但那些变系数的微分方程则更具挑战性。高阶变系数齐次微分方程没有固定的求解方法,根据变系数矩阵的不同结构类型,利用线性变换法和常数变易法求得一类变系数齐次线性微分方程组x’=A(t)x,的解,其中A(t)为n×n阶函数矩阵,且得出一类高阶变系数齐次线性微分方程组的解的一般结构。Coefficient equations with variable coefficients are more challenging than constant coefficient equations that can be easily processed with many methods.There are no fixed solution methods for the homogeneous diff erential equations of higher order.By using linear transformation and constant variation,and based on diff erent structural types of variable coefficient matrices,the solution can be obtained for a class of variable coefficient linear homogeneous diff erential equation set x’=A(t)x,in which A(t)is n×n order function matrix;by this solution,the general method can obtained for solving a class of variable coefficient linear homogeneous diff erential equation set.

关 键 词：变系数齐次线性方程组 线性变换 特征函数 

分 类 号：O175[理学—数学]