二元一阶常系数线性微分方程组的本质解法  

Essential Methods of Linear Differential Equations with Constant Coefficients of Two Variables

作　　者：赵临龙 

机构地区：[1]安康学院数学与统计学院,陕西安康725000

出　　处：《河南科学》2018年第1期6-10,共5页Henan Science

基　　金：陕西省教育厅科研项目(15JK1016);陕西省特色专业建设项目(2011-59);安康学院硕士点培育学科专项(2016AYXNZX009)

摘　　要：对于二元一阶常系数线性微分方程组:x′=Ax+f(t),引入特征根方程|A-λE|=0的特征行向量K=(k_1,k_2)(其中K满足:K(A-λE)=0)概念,将二元一阶常系数线性微分方程组,化为二元一次代数线性方程形式:(K_2x_2)′=λ(K_2x_2)+(K_2f),(K_1x_1)′=λ(K_1x_1)+K_1x_2+K_1f,从中给出原微分方程组的解.By employing the eigenvector K=(k_1,k_2)which satisfies the equations K(A-λE)=0 of the characteristic equations|A-λE|=0,the bivariate first order linear differential equations with constant coefficients would be transformed into the bivariate linear algebraic equations,which is(K_2x_2)′=λ(K_2x_2)+(K_2f),(K_1x_1)′=λ(K_1x_1)+K_1x_2+K_1f.Then combining the theories of the linear algebraic equations and the first order linear differential equations,the solutions of the original differential equations are given.

关 键 词：常系数线性微分方程组 代数线性方程 特征根 

分 类 号：O175.14[理学—数学]