二阶变系数线性齐次微分方程的通解

The General Solution of Second Order Homogeneous Linear Differential Equation with Variable Coefficient

主要讨论了二阶变系数线性齐次微分方程的求解问题,利用变量代换的方法将二阶变系数线性齐次微分方程y″+P(x)y'+Q(x)y=0化为Riccati方程,再利用已有的结果得出二阶线性变系数齐次微分方程的通解.

This article focuses on the general solution of second order homogeneous linear differential equation with variable coefficient. It uses variable substitution method to transform the second order homogeneous linear differential equation with variable coefficient y″＋P（x）y′＋Q（x）y=0 into a Riccati equation, and obtains the general solution of the second - order homogeneous linear differential equation with variable coefficients based on the results.