| 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： | 张学元.变系数二阶线性微分方程的一个新的可解类型[J].大学数学,2003,19(1):96-98. |
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| 作者姓名： | 张学元 |
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| 作者单位： | 湖南工程学院,数理系,湘潭,411104 |
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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 |
| 文章编号： | 1672-1454(2003)01-0096-03 |
| 修稿时间： | 2002年1月7日 |
A New Solvable Type of Second Order Linear Differential Equation with Variable Coefficients |
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| ZHANG Xue-yuan.A New Solvable Type of Second Order Linear Differential Equation with Variable Coefficients[J].College Mathematics,2003,19(1):96-98. |
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| Authors: | ZHANG Xue-yuan |
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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 soluable, 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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