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

2. 2 Separation of Variables

3. 3 Example 1: Find the general solution of

4. 4 Example 2: Find the general solution of

5. 5 Example 3: Find the general solution of

6. 6 Homogeneous Functions

7. 7 Homogeneous Differential Equations

8. 8 Change of Variables for Homogenous Equations

9. 9 Example 1

10. 10

11. 11 Example 2

12. 12 Example 3

13. 13 Example 4

14. 14 Orthogonal Trajectories

15. 15 Example 5

16. 16 Logistic Differential Equation

17. 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. 18 Example 6 – Deriving the General Solution Solve the logistic differential equation Solution: