| 求解高阶常系数线性微分方程的新法再探 |
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| 引用本文： | 阮述尧.求解高阶常系数线性微分方程的新法再探[J].佛山科学技术学院学报(自然科学版),1996(4). |
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| 作者姓名： | 阮述尧 |
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| 摘 要： | 把常系数齐次线性微分方程施以变换ｙ＝ｚｅｒｘ所得的方程写成复合微分方程，再转化为非齐次微分方程，用待定系数法或数学归纳法，导出了常系数齐次线性微分方程的通解是它的两个特定的互补子方程的通解的和，从而进一步导出这类微分方程的通解
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| 关 键 词： | 高阶常系数 线性微分方程通解 待定系数法 数学归纳法 |
A New Solution to the Higher Linear Differential Equation with Constant Coefficients |
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| Ruan Shuyao.A New Solution to the Higher Linear Differential Equation with Constant Coefficients[J].Journal of Foshan University(Natural Science Edition),1996(4). |
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| Authors: | Ruan Shuyao |
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| Institution: | Ruan Shuyao * |
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| Abstract: | Under the transformation y=ze rx ,the homogeneous linear differential equation was written as a composite differential equation, and then as a non homogeneous linear differential equation. By using the method of undetermined coefficients and mathematical induction, it was derived that the general solution to the homogeneous linear differentical equation with constant coefficients was the sum of the general solutions to its two specially relatively complemented subequations. |
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| Keywords: | higher linear differential equation with constant coefficients general solution the method of undetermined coefficients mathematical induction |
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