1. 39. Section 9.1 Solving Differential Equations

2. Essential Question What is a differential equation?

3. Used to formulate the fundamental laws of nature (like Newton’s Laws and laws of quantum mechanics) Differential Equations Among the most powerful tools we have for analyzing the world mathematically

4. This is the general solution. There are many specific solutions depending on initial conditions. The graphs of all of the specific solutions together are called a family of curves. Differential Equations The solution to the differential equation y’ = -2y is y = Ce -2x (We’ll learn how to do this in a few minutes)

5. Differential Equations

6. Example Only need one C

7. Example Solve when y = 1 and x = 1 Called initial condition

8. Example

9. Solve when y = 1 and x = 0

10. Assignment Pg. 521 #3-17 odd, 25, 29, 31, 39, 41