The Elementary Solving Process and the GeneralSolution to a Kind of Ordinary DifferentialEquations with Variable Coefficients of 2nd Order

Journal of Chongqing Jiaotong University(Natural Science) ›› 1990, Vol. 9 ›› Issue (3): 107-112.

The Elementary Solving Process and the GeneralSolution to a Kind of Ordinary DifferentialEquations with Variable Coefficients of 2nd Order

Hu Guoquan

Department of Basic Courses

Received:1990-02-28 Online:1990-06-23 Published:2016-11-08

一类二阶变系数常微分方程的初等解法及其通解

胡国全

基础部

作者简介:胡国全,男,35岁,讲师

Abstract

Abstract: 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.

Key words: differential equation, general solution, particular solution, equivalent equations

摘要： 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。

关键词: 微分方程, 通解, 特解, 等价方程

Hu Guoquan. The Elementary Solving Process and the GeneralSolution to a Kind of Ordinary DifferentialEquations with Variable Coefficients of 2nd Order[J]. Journal of Chongqing Jiaotong University(Natural Science), 1990, 9(3): 107-112.

胡国全. 一类二阶变系数常微分方程的初等解法及其通解[J]. 重庆交通大学学报（自然科学版）, 1990, 9(3): 107-112.

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