二元一阶常系数线性微分方程组的新解法

摘要

By employing the eigenvector K=(k1,k2) which satisfies the equations KT(A-λE)=0 of the characteristic equations |A-λE |=0,the bivariate first order linear differential equations with constant coefficients can be transformed into the bivariate linear algebraic equations k1x1+k2x2=C1eλt+eλt∫(k1 f1+k2 f2)e-λtdt . 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.%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=(k1,k2)(其中K满足:KT(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:k1x1+k2x2=C1eλt+eλt∫(k1 f1+k2 f2)e-λtdt,并结合代数线性方程和一阶线性微分方程的理论,给出原微分方程组的解.