一类二阶变系数常微分方程的初等解法及其通解

The Elementary Solving Process and the GeneralSolution to a Kind of Ordinary DifferentialEquations with Variable Coefficients of2nd Order

本文针对变系数P(t)与q(t)之间的某种确定的函数关系,通过简便的初等积分,将直接给出有关二阶变系数非齐线性微分方程:x″+P(t)x′+q(t)x=f(t)的通解。

For a certain function relation between the variable coefficient p(t) and q(t), the general solution to an inhomogeneous linear differential equation of second order x'+p(t)x'+q(t)x=f(t) can be directly found by the simple elementary integration in this paper.