1. (1) The order of ODE: the order of the highest derivative e.g., Chapter 14 First-order ordinary differential equation (2) The degree of ODE: After the equation has been rationalized, the power of the highest-order derivative. e.g., (3) The general solution of ODE contains constants of integration, that may be determined by the boundary condition. (4) Particular solution: The general solution contains the constants which are found by the boundary condition. (5) Singular solution: Solutions contain no arbitrary constants and cannot be found from the general solution.

2. with n parameters satisfies an nth-order ODE in general. The boundary conditions on the solutions determine the parameters. Chapter 14 First-order ordinary differential equation 14.1 General form of solution Ex: Consider the group of functions

3. Chapter 14 First-order ordinary differential equation 14.2 First-degree first-order equation Separable-variable equation

4. Chapter 14 First-order ordinary differential equation Exact equations

5. Chapter 14 First-order ordinary differential equation

6. Inexact equations: integrating factors

7. Chapter 14 First-order ordinary differential equation

8. Linear equations

9. Chapter 14 First-order ordinary differential equation

10. Homogeneous equations

11. Chapter 14 First-order ordinary differential equation

12. Isobaric equations

13. Chapter 14 First-order ordinary differential equation Bernoulli’s equation

14. Chapter 14 First-order ordinary differential equation

15. Miscellaneous equations Chapter 14 First-order ordinary differential equation

17. 14.3 Higher-degree first-order equation Chapter 14 First-order ordinary differential equation

20. Clairaut’s equation