1

6.1 and 6.2 - Differential EquationsDifferential equations are used in a variety of fields including physics, biology, engineering, and economics. Differential equations are used to model and experiment with radioactive decay, population growth, Newton's Law of Cooling, and rates of compound interest.

Solve for a general solution.

Then solve with the initial condition (2,1).

Example 1:

2

Solve through (3,1)

Example 2:

3

Example 3:

If , find a specific solution through (0,1)

4

Example 4:

Solve for a general solution

5

Slope FieldsRecall Example 1 when we represented the solution of the differential equation algebraically. This solution can also be represented graphically.

X Y dy/dx

This is #1 on Slope Fields Packet

6

X Y dy/dx

Draw a partial slope field for the following differential equation to represent the general solution graphically.

This is #2 on Slope Fields Packet

7

X Y dy/dx

Draw a partial slope field for the following differential equation to represent the general solution graphically.

This is #3 on Slope Fields Packet

8

X Y dy/dx

Draw a partial slope field for the following differential equation to represent the general solution graphically.

This is #4 on Slope Fields Packet

9

X Y dy/dx

Draw a partial slope field for the following differential equation to represent the general solution graphically.

This is #5 on Slope Fields Packet

10

X Y dy/dx

Draw a partial slope field for the following differential equation to represent the general solution graphically.

This is #6 on Slope Fields Packet

11

12

13

14

15

21. 22. 23. 24.

16

25. 26. 27. 28.

17

29.

18

30.

19

31.

20

32.

21

Review of Exponent Laws and Log Rules:

=

=

=

=

22

33.

2006 AP Calculus AB FRQ #5

23

24

2008 AP Calculus AB FRQ #5

34.

25