二階變系數(shù)非齊次線性微分方程的一類通解

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【摘   要】   利用待定函數(shù)法研究了二階變系數(shù)非齊次線性微分方程的系數(shù)滿足特定條件時的通解公式。旨在豐富二階線性微分方程的解題技巧，培養(yǎng)學(xué)生的創(chuàng)新思維能力。

【關(guān)鍵詞】   變系數(shù)；非齊次；微分方程；解題技巧

A Class of General Solutions for Second-order Non-homogeneous Linear Differential Equations with Variable Coefficients

Liu Mengmeng， Ye Yongsheng*， Shi Yangyang

（Huaibei Normal University， Huaibei 235000， China）

【Abstract】    In this paper， the undetermined function method is used to study the general solution formula of the second order non-homogeneous linear differential equation with variable coefficients when the coefficients meet certain conditions. The purpose is to enrich the skills of solving second-order linear differential equations and to cultivate students' innovative thinking ability.

【Key words】     variable coefficient; non-homogeneous; differential equation; problem-solving skill

〔中圖分類號〕  O175；G642                       〔文獻(xiàn)標(biāo)識碼〕  A              〔文章編號〕 1674 - 3229（2024）03- 0125 - 04

0     引言

二階變系數(shù)非齊次線性微分方程

[y″+p（x）y′+q（x）y=f（x）]                     （1）

其中[p（x）]，[q（x）]以及[f（x）≠0]為[x]的連續(xù)函數(shù)。（剩余3632字）