某些非线性常微分方程的常数变易法_数学毕业论文（可编辑）.docVIP

某些非线性常微分方程的常数变易法_数学毕业论文 Abstract Constant variation method is a special method of solving diferential equation.It is simpler to use constant variation method to get some special solutions.Several 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 theoremsSolutions to some kinds of second-order differenfial equations by using variable transformation method are given and the scope of applications is expanded.Meanwhile, the integral types of differential equations are provided and the expressions of reduction of integrals to a common 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 expression of the general solution. Key words:ordinary differential equation; the method of constant variation; non ? linear; second?order nonlinear differential equation;variable transformation integral type reduction of integrals to a common denominator 目 录 第1章 绪论 1 1.1 引言 1 1.2 本文的主要研究内容 4 第2章 一阶非线性常微分方程的常数变易法与举例 5 2.1 一阶非线性常微分方程的常数变易法 5 2.1.1 基本类型Ⅰ ……………………………………………………5 2.1.2 基本类型Ⅱ …………………………