1 6.3 Separation of Variables and the Logistic Equation Objective: Solve differential equations that can be solved by separation of variables.

2 Separation of Variables

3 Example 1: Find the general solution of

4 Example 2: Find the general solution of

5 Example 3: Find the general solution of

6 Homogeneous Functions

7 Homogeneous Differential Equations

8 Change of Variables for Homogenous Equations

9 Example 1

10

11 Example 2

12 Example 3

13 Example 4

14 Orthogonal Trajectories

15 Example 5

16 Logistic Differential Equation

17 Logistic Differential Equation If y is greater than L, then dy/dt < 0, and the population decreases. The graph of the function y is called the logistic curve.

18 Example 6 – Deriving the General Solution Solve the logistic differential equation Solution: