文档介绍：摘要
常数变易法是求解微分方程的一种特殊方法,利用常数变易法在解决某些方程特解时简便易用。列举了几种常数变易法区别于教材中的一些用法,并比较了此方法在某些方面的优劣。
常数变易法是求解一阶非齐次线性常微分方程行之有效的方法。本文从求解一类特殊形式的一阶常微分方程入手,证明了变量分离方程、Bernoulli方程、部分齐次方程以及其它形式的一阶非线性常微分方程可用常数变易法求解,从而将常微分方程中的常数变易法用于更加广泛的地发去。
阅读理解首次积分求得的六个定理以及推论,将六个类型的方程与常数变易法相结合,并对定理运用常数变易法进行证明,求解。
应用变量变换方法,解几类可化为分离变量的二阶非线性微分方程,扩大了变量变换方法的使用范围,提供微分方程的可积类型,给出几个通积分的表达式。
二阶线性微分方程在实际问题中有着广泛的应用。本文利用常数变易法对二阶非线性微分方程进行讨论后, 给出了求其通解表达式的具体方法。
关键词:常微分方程; 常数变易法; 非线性;二阶非线性;可积类型;通解分。
Abstract
Constant variation method is a special method of solving diferential is simpler to use constant variation method to get some special constant variation methods different from those in textbooks are listed here to find out their advantages and disadvantages in some aspects.
The method of constant variation is an effective way to solve the first order non - homogeneous linear ordinary differential equation. This paper studies the first order ordinary differential equation in a special form, and proves that the equation of variable divided, Bernoulli equation, some non - homogeneous equations and the first order non – linear ordinary differential equation in another form can all be solved with this method, and then popularizes the method of constant variation.
Reading the six obtained by the first integral theorem and corollary, With six types of equations and constant variation, I use the constant variation to prove, to solve theorems.
Solutions to some kinds of second-order differenfial equations by using variable
transformation method are given and the scope of applications is , the integral types of differential equations are provided and the expressions of reduction of integrals to mon denominator are also given.
The Second-order Linear Homogeneous Equation is widely used in practical problems. The paper discusses the second-order non-linear homogeneous differential equation“”by the constant-variation method, and presents some specific methods on the e