| 变系数二阶线性微分方程的一个新的可解类型 |
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| 引用本文： | 胡爱莲,宋爱丽.变系数二阶线性微分方程的一个新的可解类型[J].河南科学,2008,26(11). |
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| 作者姓名： | 胡爱莲 宋爱丽 |
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| 作者单位： | 喀什师范学院,数学系,新疆,喀什,844000 |
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| 基金项目： | 新疆高等学校科研项目，喀什师范学院校内课题 |
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| 摘 要： | 通过双变换——未知函数的线性变换和自变量变换,将一类变系数线性微分方程化为二阶常系数线性微分方程,从而得到变系数二阶线性微分方程的一个新的可解类型,推广了著名的二阶Euler方程.
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| 关 键 词： | 变系数二阶线性微分方程 双变换 新的可解类型 通解 |
A New Solvable Type of Second Order Linear Differential Equation with Variable Coefficients |
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| Hu Ailian,Song Aili.A New Solvable Type of Second Order Linear Differential Equation with Variable Coefficients[J].Henan Science,2008,26(11). |
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| Authors: | Hu Ailian Song Aili |
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| Abstract: | In this paper,a kind of linear differential equation with variable coefficients is turned into second order linear differential equation with constant coefficients through double transformation—linear and self-variable transformation of unknown function,then a new solvable type of second order linear differential equation with variable coefficients is obtained.Thus,the famous second order Euler equation is expanded. |
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| Keywords: | second order linear differential equation with variable coefficients double transformation new solvable type general solution |
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