1. MAT 1235 Calculus II Section 9.3 Separable Equations I http://myhome.spu.edu/lauw

2. HW and … WebAssign 9.3 Part I (15 problems, 123min.) Wednesday: 9.5 Thursday: 9.3 Part II

3. Differential Equations

4. Many “phenomenon” can be modeled /described by D.E.

5. Example 0.1 (Chemistry) Reaction

6. Example 0.2

7. Example 0.3 Pendulum

8. Example 0.4 q = charge on the capacitor

9. Toolbox Approach Given a differential equation Identify the type/nature of the differential equation. Use the specified techniques to solve for the solutions.

10. Separable Equations Technique: Separation of Variables

11. Example 1

12. 1. is called the general solutions of the D.E. 2. We can verify the solution by differentiation. Remarks

13. 3. The value of C can be fixed if additional condition is given. e.g. y(0)=4 (initial condition) Remarks

14. 3. The value of C can be fixed if additional condition is given. e.g. y(0)=4 (initial condition) 4. is called the particular solution of the D.E. Remarks

15. Solution Curves

16. Example 2

17. Remarks

18. Example 2

19. Example 3