本教材共分为5章，具体介绍一阶常微分方程初等解法，齐次线性微分方程一般解法、非齐次线性微分方程的常数变易法、非齐次线性微分方程伯努利方程解法，一阶常微分方程积分因子求法以及四类隐式微分方程的解法，一阶微分方程的解的存在性定理以及延拓性定理，高阶微分方程的常数变易法以及非齐次（齐次）常系数高阶微分方程的解法（待定系数法），变系数高阶微分方程的解法，矩阵指数求法，一阶线性微分方程组解的结构以及解的存在性定理，非线性微分系统的稳定性理论等知识点。
Chapter 1 Elementary Integration Methods
1.1 Differential equations and solutions
1.2 Variable separable equation
1.3 Homogeneous differential equations
1.4 First-order linear differential equations
1.5 Total differential equations and integration factors
1.6 First-order implicit differential equation
1.7 Several high-orderequations
Chapter 2 Fundamental Theorems.
2.1 Existence and uniqueness theorem
2.2 Theorem of existence and uniqueness of solution
2.3 Extension of the solution
2.4 Strange solution
2.5 Continuous dependence on initial value of the solution
Chapter 3 Linear Differential Equations
3.1 First order differential equations
3.2 General concepts of first-order linear differential equations
3.3 General theory of first-order linear homogeneous systems
3.4 General theory of first-order linear non-homogeneous systems
3.5 Solution of linear differential equations with constant coefficients
3.6 The solution method for linear differential equations(complex and multiple root)
Chapter 4 Linear Differential Equations
4.1 General theory of n-order linear differential equations
4.2 Solution of n-th order constant coefficient linear homogeneous equation
4.3 N-th order constant coefficient linear non-homogeneous equation solution
4.4 Second-order constant coefficient linear equations and vibration phenomena
Chapter 5 Introduction to Qualitative and Stability Theory
5.1 Concept of stability
5.2 Lyapunov's second method
5.3 Basic concepts of plane autonomous system
5.4 Introduction to plane qualitative theory
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