(高等数学英文课件）6.5 Linear First-Order Differential Equations[精].ppt

Chapter 6 Transcendental Functions and Differential Equations
Derivatives of Inverse Trigonometric
Functions; Integrals
Logarithms
Exponential Functions
First-Order Separable Differential Equations
Linear First-Order Differential Equations
Euler’s Method; Population Models
Hyperbolic Functions

Linear First-Order Differential Equations
(一阶线性微分方程)
1. Definition
2. Classification
homogeneous
nonhomogeneous
Separate the variables
Integrate both sides
The solutions
Solution to the homogeneous equations
Using the method of variation of constants(常数变易法)
That is to say
The solutions
Solution to the nonhomogeneous equations
Example 1. Solve the differential equation
Solution.
Example 2. Solve the differential equation
Solution 1.
Solution 2.
Exercises
P506 4, 7, 17, 19.