基于Riccati方程的一阶线性微分方程组的基解矩阵

Fundamental Matrix of the First Order Linear Differential Equations Based on the Riccati Equation

文章基于Riccati方程的解,研究了其与一类变系数线性微分方程组一个非零解间的关系,在此基础上给出了这一类变系数线性微分方程组的基解矩阵的计算公式.

As we all known, the structure of solutions for the varying - coefficient linear differential equations has been very perfect in theory, but there is not general method for concrete solutions of the fundamental matrix to follow. In the paper, relationship between solutions of the Riccati equation and a non - zero solution of the first kind varying - coefficient linear differential equations is analyzed, then the calculate formula for fundamental matrix is given out.