发布时间 : 星期一 文章二阶常微分方程的解法及其应用三稿更新完毕开始阅读5e4e6af2f01dc281e43af03e
本科毕业论文 二阶常微分方程的解法及其应用 学生姓名： 指导教师： 所在院系： 数学教育系 所学专业年级： 数学与应用数学2009级 中国·长春 2013年 5 月
目 录
1 引言 ........................................................................................................................................ - 5 - 2 二阶常系数常微分方程的几种解法 ............................................................................ - 5 - 2.1特征方程法 ...................................................................................................................... - 5 - 2.1.1 特征根是两个实根的情形 ..................................................................................... - 6 - 2.1.2 特征根有重根的情形 .............................................................................................. - 6 - 2.2常数变易法 ...................................................................................................................... - 8 - 2.3拉普拉斯变换法 ............................................................................................................. - 9 - 3 常微分方程的简单应用 ................................................................................................. - 10 - 3.1 特征方程法 ................................................................................................................... - 11 - 3.2 常数变易法 ................................................................................................................... - 13 - 3.3 拉普拉斯变换法 .......................................................................................................... - 14 - 4 总结及意义 ........................................................................................................................ - 15 - 参考文献 ................................................................................................................................. - 16 -
二阶常微分方程的解法及其应用
摘要：本文主要介绍了二阶常系数微分方程的三种解法：特征方程法、常数变异法和拉普拉斯变换法，并着重讨论了特征方程根为实根、复根及重根的情形。针对这三种解法的特点，分别将其应用到求解弹簧振子系统的振子的运动方程。
关键词：二阶常微分方程;特征根法；常数变异法；拉普拉斯变换
METHODS FOR TWO ORDER ORDINARY DIFFERENTIAL
EQUATION AND ITS APPLICATION
Abstract:This paper mainly introduces three kinds of solution for two order differential equation with constant coefficients: the characteristic equation method, the method of variation of constant and Laplasse transform method, and discusses the characteristics of Fang Chenggen is the real root, complex roots and root. According to the characteristics of the three solution, were applied to the equations of motion of vibrator for spring oscillator system.
Keywords:second order ordinary differential equation; Characteristic analysis; constant variation method; Laplasse transform