二阶变系数齐线性常微分方程的求解

Solution to Second-order Homogeneous-linear Ordinary Differential Equations with Variable Coefficients

给出了二阶变系数齐线性常微分方程一种新的求解方法.将二阶变系数齐线性常微分方程问题转化为Riccati方程来求解,讨论了二阶变系数齐线性常微分方程的通解和初值问题,得到初值问题近似解的理论基础、计算方法和误差估计.

This paper presents a new method of solution to the second order homogeneous linear ordinary differential equation with variable coefficients. The second-order homogeneous linear ordinary differential equation with variable coefficients can be translated to Riccati equation and its general solution and initial value problem were discussed. The basic principle, calculating method and error estimation were obtained about approximate solution of initial value problem.