1. and Indefinite Integration (Part II)
4.1: Antiderivatives
and Indefinite Integration (Part II)
Greg Kelly, Hanford High School, Richland, Washington

2. Objectives Write the general solution of a differential equation.
Find a particular solution of a differential equation.

3. General solution for various values of C for

4. To find a particular solution, you need to know the value of y=F(x) for one value of x.
This information is called an initial condition.

5. Find the particular curve that passes through the point (2,4).

6. Find the general solution of
Find the particular solution that satisfies the initial condition F(1)=0.

7. A ball is thrown upward with an initial velocity of 64 ft/sec from an initial height of 80 feet.
a.) Find the position function giving the height as a function of the time t.
Using the formula:

8. A ball is thrown upward with an initial velocity of 64 ft/sec from an initial height of 80 feet.
a.) Find the position function giving the height as a function of the time t.
Without using the formula:

9. A ball is thrown upward with an initial velocity of 64 ft/sec from an initial height of 80 feet.
When does the ball hit the ground?

10. Examples:

11. Examples:

12. (51 & 53 find particular solution only)
Homework
4.1 (page 256)
# 47, 49, 51, 53
57 – 65 odd,
71, 75 – 83 odd
(51 & 53 find particular solution only)