| 关于常数变易法求一阶线性非齐次微分方程通解的两点思考 |
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| 引用本文： | 汪维刚.关于常数变易法求一阶线性非齐次微分方程通解的两点思考[J].安庆师范学院学报(自然科学版),2012,18(2):105-107. |
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| 作者姓名： | 汪维刚 |
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| 作者单位： | 桐城师范高等专科学校,安徽桐城,231402 |
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| 摘 要： | 利用常数变易法求出的一阶线性非齐次微分方程的通解公式不严谨,产生的原因在于不恰当地使用不定积分取代定积分。审视常数变易法的"变易"过程,发现除此之外,"变数变易法"也是一种求一阶线性非齐次微分方程通解的方法。
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| 关 键 词： | 一阶线性非齐次微分方程 通解 常数变易法 增根 变数变易法 |
Two - point Consideration on the General Solution of One - step Linearity Nonhomogenous Differential Equation by Constant Variation Method |
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| WANG Wei-Gang.Two - point Consideration on the General Solution of One - step Linearity Nonhomogenous Differential Equation by Constant Variation Method[J].Journal of Anqing Teachers College(Natural Science Edition),2012,18(2):105-107. |
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| Authors: | WANG Wei-Gang |
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| Institution: | WANG Wei-Gang(Tongcheng Teachers College,Tongcheng,Anhui 231402,China) |
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| Abstract: | The formula of ordinary solution of one-step linearity nonhomogenous differential equation which is extracted by using the constant change law is not rigorous that the reason produced lay in which has used the indefinite integral to substitute for the definite integral not appropriately.Carefully the paper examines the process of "changing" of the solution by constant change law,and discoveres in addition that "the variable change law" also is one kind method by which strives for ordinary solution of one-step linearity nonhomogenous differential equation. |
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| Keywords: | the one -step -linearity -nonhomogenons differential equation general solution constant variation method ex- traneous root inconstant variation method |
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