| 二阶变系数线性微分方程的通解 |
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| 引用本文： | 王伟.二阶变系数线性微分方程的通解[J].新乡学院学报(自然科学版),2011(4):301-302. |
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| 作者姓名： | 王伟 |
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| 作者单位： | 扬州工业职业技术学院基础部 |
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| 摘 要： | 利用特解讨论了二阶变系数齐次线性微分方程,得到了形如y=y^＊{c1∫（y^＊）^-2exp-∫p（x）dx]dx＋c2}的通解公式,同时,利用常数变易法得到了非齐次方程的通解,改进和推广了相关文献中的结论。
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| 关 键 词： | 通解 特解 二阶线性变系数微分方程 |
The General Solution of Second Order Linear Differential Equations with Variable Coefficient |
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| Authors: | WANG Wei |
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| Institution: | WANG Wei(Department of Basic Courses,Yangzhou Polytechnic Institute,Yangzhou 225127,China) |
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| Abstract: | A second order linear differential equation with variable coefficient has been studied, and a general solution is given by use of the special solution, as follows y=y^＊{c1∫（y^＊）^-2exp-∫p（x）dx]dx＋c2}. Meanwhile, the general solution of inhomogeneous equation is given by use of the method of variation of constant. Some recent results in relative articles are extended and improved. |
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| Keywords: | general solution special solution second order linear differential equations with variable coefficient |
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