1. 5014 - Differential Equations BC CALCULUS

2. Differential Equations Defn: An equation that contains a derivative ( or a function and a derivative ) is called a Differential Equation. EX: or The most famous might be: AP requires only Separable Diff Eq’s.

3. Type A: Explicit We did these last semester as Initial Value Problems with Anti- derivatives. Illustration: “Separate the variables” or Write in Differential form. Integrate both sides. Add the +c’s and put on the dominant side.

4. Type B: Implicit AP requires only “separable.” Illustration:

5. Example: Find the GENERAL and PARTICULAR Solutions.

6. Example 2: 1973 AB Exam. If and y = 4 when x = 0, then y =

7. Example: AP Type Find the GENERAL and PARTICULAR Solutions. BREAK HERE IN CASE OF EMERGENCY ! REM: the Diff.Eq. must be a product !

8. Example 2: AP Type Find the GENERAL Solution.

9. Example 3: AP Type Find the PARTICULAR Solution.

10. VERIFY Objective: To show (verify) a given function is a solution to a Differential Equation. Rem: ALGEBRA I To show a point is a solution to a system of equations, plug in the point and check if the equations are true or false. Is ( 2, -3 ) a solution to

11. Illustration: Objective: To show (verify) a given function is a solution to a Differential Equation. Illustration: Show is a solution to. Find and substitute both y and into the equation.

12. Example: Verify that is a solution to

13. DAY ONE: TEXT6.1 p.327 1-23 odd 6.4 p.3571-13 odd