00后大学生：微分方程是什么？

任何一位00后大学生，如果对微分方程有兴趣，进入互联网大课堂，搜索“微分方程章节”，在数秒钟时间内，即可得到如下附件所述结果，值得参考，不论深夜或是上午，也不论今年或明年，更不论你在北京或南京。互联网大课堂，难道不是大宝贝？

袁萌   6月19日

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第845页：微分方程

14  DIFFERENTIAL EQUATIONS

14.1 EQUATIONS WITH SEPARABLE VARIABLES（一阶分离变量微分方程）

A first order diferential equation is an equation involving an independent variable t, a dependent variable y, and the derivative dy/dt. In many applications, the independent variable t is time. A first order differential equation can be put in the following form, where f(t, y) is continuous in both t and y.

FIRST ORDER DIFFERENTIAL EQUATION

(1)

dy /dt = f(t, y).

For instance, if tis time and y is the position of a particle at time t, the differential equation (1) gives the velocity y of the particle in terms of time and position. A differential equation gives information about an unknown function y(t). The general solution of a first order differential equation is the family of all functions y(t) that satisfy the equation. Each function in this family is called a particular solution of the differential equation. In most cases, the family of functions will depend in some way on a constant C, and the graphs of these functions will form a family of curves that fill up the (t, y) plane but do not touch each other, as in Figure 14.1.1. Some ……（以下省略）