Separable Equations:

1 order equations with separable variable
written in the form: f(x)dx=g(y)dy (seperate the variables and intergration)

eg： y=q(x)

进行积分

H(y) = G(x) + c
Both are antiderivatives of p(y) = 1/h(y) and g(x)

a dy=b dx
等式两边直接积分
求解， … = … +c
词汇：
 Strictly monotonic 严格单调
 Critical point 临界点
 Phase portrait 相位图
 Phase line 相线
 Autonomous de： dy/dt = f(y), function of y, not t
 
2021.1.7
                                    ODE – Autonomous Equations and Stability
Autonomous Equation
is an equation of the special form
x′=f(x)(1)
x'=f(x) \qquad (1)
x′=f(x)(1)
Note: 可以看出这个方程于函数x(t)x(t)x(t)的自变量ttt无关
Direction field
因为与自变量无关...