大一高数空间向量笔记（歪歪不挂高树4）

分享兴趣，传播快乐，增长见闻，留下美好!

亲爱的您，这里是Learning Yard学苑。

今天小编为大家带来"微分方程再识”，欢迎您的访问。

Share interest, spread happiness, increase knowledge, leave beautiful!

Dear, this is Learning Yard.

Today Xiaobian brings you "Differential equations re-acquaintance", you are welcome to visit.

文接上回，开学良久，相信大家学习生活也步入正轨了，今天歪歪就来为大家讲讲微分方程这一章节后半部分吧！

The article continues from the last time, the school has been started for a long time, I believe that everyone's study life has also entered the normal, today I will talk about the second half of this chapter of differential equations for you!

一.什么是微分方程

One. What are differential equations

基本概念：微分方程指的是：含有未知函数及其导数的方程。

Basic concept: A differential equation is an equation that contains an unknown function and its derivatives.

二.高阶线性微分方程

高阶微分方程定义：二阶及二阶以上的微分方程称为高阶微分方程。

Two. Higher-order linear differential equations

Definition of higher-order differential equations: Differential equations of the second order and above are called higher-order differential equations.

三.解题技巧讲解

考点总览

Three. Explanation of problem-solving skills

Overview of the test center

1.

此类型右端仅含有自变量x，只要对两端不断积分便可得到所求目标函数

即：

The right end of this type contains only the independent variable x, and the objective function can be obtained by continuously integrating the two ends

Namely:

2.

此类型微分方程，由于右段不显含未知函数y，所以我们设y'=p，具体解法如下：

For this type of differential equation, since the right segment does not contain an unknown function y, we set y'=p, and the specific solution is as follows:

3.

在此方程中不明显的含自变量x，为了求出它的解，我们依旧令y'=p，并利用复合函数的求导法则把y''化为对y的倒数

即：

In order to find its solution for the independent variable x, which is not obvious in this equation, we still let y' = p and use the derivation of the composite function to turn y'' into the reciprocal of y

Namely:

最后，以上就是今天分享的可降阶的高阶微分方程求解三大方法，希望各位友友们能熟练掌握此方法，提升高数能力。

Finally, the above are the three major methods of solving lower-order higher-order differential equations shared today, I hope that you can master this method and improve your ability to high numbers.

今天的分享就到这里了

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参考资料：百度百科-秒懂百科、《高等数学辅导及习题精解》、《高等数学第七版上册》

翻译：有道翻译

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文字|歪歪

排版|歪歪

审核|闫庆红

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