| 林庆泽.利用微分算子法研究二阶齐次线性微分方程与Riccati方程通解之联系[J].海南师范大学学报自科版,2017,30(3):237-242 |
| 利用微分算子法研究二阶齐次线性微分方程与Riccati方程通解之联系 |
| Study on the Relation between the General Solutionsof the Second Order Homogeneous Linear Differential Equationand the Ones of Riccati Equation by Differential Operator Method |
| 投稿时间：2017-01-14 |
| DOI：10.12051/j.issn.1674-4942.2017.03.001 |
| 中文关键词: 算子法 微分方程 Riccati方程 通解 |
| 英文关键词: operator method differential equation Riccati equation general solution |
| 基金项目: |
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| 摘要点击次数: 697 |
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| 中文摘要: |
| 文章应用微分算子法处理二阶变系数线性微分方程，揭示了二阶齐次变系数线
性微分方程与Riccati方程的通解理论之间的联系，发现这两类方程之间的通解可以互相转
化，同时给出转化的途径.最后，作为理论的应用分析了一些具体例子. |
| 英文摘要: |
| The second-order linear differential equations with variable coefficients are processed by differential operator
method , and the relation between the general solutions of the second-order homogeneous linear differential equations with
variable coefficients and the ones of Riccati equations is revealed. Then , the conclusion that the general solutions between
the two equations can be transformed into each other is deduced and the way of transformation is given. Finally , some examples
are given as theoretical applications. |
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