二阶常微分方程的解法分析研究 数学与应用数学专业VIP专享

摘要：本文主要是介绍了二阶常微分方程众多解法中的三种，分别为特征方程法，拉普拉斯变换法和常数变易法，研究并讨论了二阶常微分方程在特征方程法中特征方程根为实根，复根和重根的情形。我们选用了弹簧振子系统的振子运动，用这三种不同的方法来解决该问题。关键词：二阶常微分方程；特征根法；常数变易法；拉普拉斯变换Abstract: The main purpose of this paper is the second-order ordinary many differential equation solution of three, respectively as the characteristic equation method, Laplace transform method and variation of constants method, study and discuss the second-order often differential equation in the characteristic equation of the roots of the characteristic equation for real roots, complex roots and root weight. We choose the spring oscillator the oscillator motion, these three different methods to solve the problem.Keywords: second order ordinary differential equation; Characteristic analysis; constant variation method; Laplasse transform目录1 绪论.........................................................31.1 二阶常微分方程的起源和发展史......................................31.2 二阶常微分方程的介绍..............................................31.3 研究二阶常微分方程的目的与意义....................................42 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......................................5 2.1.2 特征根有重根的情形..........................................62.2 常数变易法........................................................72.3 拉普拉斯变换法....................................................93 二阶常微分方程解法的应用（分析例题）........................113.1 特征方程法.......................................................113.2 常数变易法.......................................................133.3 拉普拉斯变换法...................................