| 微分方程两种不同形式特解结果的比较分析 |
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| 引用本文： | 钱琳琳,李秀丽,牛瑞燕,李平.微分方程两种不同形式特解结果的比较分析[J].北京联合大学学报(自然科学版),2005,19(4):21-23. |
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| 作者姓名： | 钱琳琳 李秀丽 牛瑞燕 李平 |
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| 作者单位： | 北京联合大学,自动化学院,北京,100101;北京联合大学,自动化学院,北京,100101;北京联合大学,自动化学院,北京,100101;北京联合大学,自动化学院,北京,100101 |
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| 摘 要： | 线性常系数非齐次微分方程是LTI连续时间系统的数学模型.以输入信号为f(t)=e-2t的二阶微分方程为例,分析了两种不同形式的特解:yp(t)=p1te-2t p2e-2t和yp(t)=te-2t,并从应用角度、物理意义等方面对二者进行了比较.
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| 关 键 词： | 微分方程 特解形式 自由响应 强迫响应 |
| 文章编号： | 1005-0310（2005）04-0021-03 |
| 收稿时间： | 2005-07-01 |
| 修稿时间： | 2005年7月1日 |
The Comparison Between Two Patterns of Particular Solution of Differential Equation |
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| QIAN Lin-lin,LI Xiu-li,NIU Rui-yan,LI Ping.The Comparison Between Two Patterns of Particular Solution of Differential Equation[J].Journal of Beijing Union University,2005,19(4):21-23. |
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| Authors: | QIAN Lin-lin LI Xiu-li NIU Rui-yan LI Ping |
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| Institution: | Automation College of Beijing Union University, Beijing 100101, China |
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| Abstract: | Liner invariant co-effect non-homogenous differential equation is the mathematical model of LTI continuous system.For the equation with such input as f(t)=e~(-2t),its particular solution has two patterns,which are y_p(t)=te~(-2t) and y_p(t)=p_1te~(-2t)+p_2e~(-2t).It analyzed the two patterns of particular solutions in terms of application and physical meaning. |
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| Keywords: | differential equation patterns of particular solution free response compulsory response |
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