Application of Second Order Real Matrix to Plane Autonomous Linear Ordinary Differential Equation

Abstract

According to the matrix standard form of the second order real matrix, we study the qualitative issue of the planar autonomous linear ordinary differential equation, construct the qualitative optimization system which is admissible by the equation, and carry out symmetry reduction. At the same time, the solution method of second order real square matrix for the plane autonomous linear ordinary differential equation is given in the Bergman space. The approximate solutionis obtained by truncating the exact solutionin the Bergman space. In the end, the standard type of the plane autonomous linear ordinary differential equations is summed up and the exact solutions of the plane autonomous linear ordinary differential equations are given in combination with an example.