| 一阶线性非齐次微分方程求解方法的讨论和一个简化的求解方法 |
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| 引用本文： | 徐宝钢. 一阶线性非齐次微分方程求解方法的讨论和一个简化的求解方法[J]. 辽宁工程技术大学学报(自然科学版), 1987, 0(4) |
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| 作者姓名： | 徐宝钢 |
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| 作者单位： | 阜新矿业学院数学教研室 |
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| 摘 要： | 本文证明了一阶线性非齐次微分方程y＇+P(x)·y=f(x)三个求解方法:参数变易法、积分公式、积分因子法之间的等同关系.从参数变易法中引出一个简化的积分公式.事实上此公式恰是对用参数变易法解高阶线性非齐次微分方程时对n=1的拓广.最后以实例验证此公式的简易.
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| 关 键 词： | 线性非齐次微分方程 正规形微分方程 参教变量法 积分因子 |
THE EXPLORATION OF SOLUTION ON THE LINEAR NON-HOMEOGENEOUS DIFFERENTIAL EQUATION AND A SIMEPLE METHOD OF SOLUTION |
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| Xu Baogang. THE EXPLORATION OF SOLUTION ON THE LINEAR NON-HOMEOGENEOUS DIFFERENTIAL EQUATION AND A SIMEPLE METHOD OF SOLUTION[J]. Journal of Liaoning Technical University (Natural Science Edition), 1987, 0(4) |
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| Authors: | Xu Baogang |
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| Abstract: | This paper shows three methods to find out lthe inear non-homeogeneous differential equation of first order - y1 + p(x(y = f(x): the equal relations among the parameter variation , integral formula and integral factor. The simple integral formula is given from the paramter variation. In fact, this formula is wide to n = 1 when it is used to solve the linear non-homeogeneous differential equation of high order.Finally,this furmula is, with illustration tested to be simple and easy. |
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| Keywords: | linear non-homeogeneous differential equation regular differential equation the equal relations among the parameter variation integral factor |
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