精品文档---下载后可任意编辑[摘要]微分方程是讨论自然科学和社会科学中的事物、物体和现象运动、演化和变化规律的最为基本的数学理论和方法.而一阶微分方程作为微分方程的基础问题，是解决其他问题的重要环节.本文总体分为两个环节：第一部分介绍了一阶显式微分方程的多种解法，深化讨论了可分离变量的方程，可化为变量可分离方程的齐次方程，一阶线性微分方程，恰当方程，积分因子法这些特别类型.本文的另一部分介绍了一阶隐式微分方程的多种结合，结合可解出 y，结合可解出 x，不显含 y 的隐式方程，不显含 x 的隐式方程这四类特别的情况进行探讨.文章的最后一部分则是选取了一阶微分方程的四类非常特别的微分方程，给出了各种通解.[关键词]显式微分方程，可分离变量，一阶线性微分方程，齐次方程，隐式微分方程精品文档---下载后可任意编辑The Method for First-order Differential EquationsStudent: Wu Tao ,School of Information and MathematicsTutor: Wu Haitao ,School of Information and Mathematics[Abstract]Differential equations isthe most basic mathematical theory and methods to study the natural sciences and the social sciences things, objects and phenomena movement, evolution and variation.The first order differential equations as a basis for the problem, and is an important part of solving other problems.This paper is divided into two areas overall：The first part introduces many kinds of solutions of differential equations of first-order explicit, it discusses the Variable separable equation in depth,The homogeneous equation can be separated equations for variables,First order linear differential equations, The appropriate equations ,Integral factor method,and so on.Another part of the article describes the combination of a variety of first-order differential equations implicit,Y can be solved in conjunction,X can be solved in conjunction,The implicit equation without Y,The implicit equation without X,These four kinds of special cases are discussed in this pape...
