1. Section 6-1 continued Slope Fields

2. Definition A slope field or directional field for a differentiable equation is a collection of short line segments with the same slope as the solution curve through a given point (x,y)

3. Definition A slope field shows the general shape of all the solutions of a differential equation

4. 6.Sketch a slope field for for the points (-1, 1) (0, 1) and (1, 1)

5. 7.Sketch a slope field for through the point (1, 1) x-2 001122 y 1 1 1 1 1 y’=2x+y

6. A slope field or direction field consists of line segments with slopes given by the differential equation. These line segments give a visual perspective of the slopes of the solutions of the differential equation. a)Sketch using pencil two approximate solutions of the differential equation on the given slope field, one of which passes through the indicated point b)Use integration to find the particular solution of the differential equation and use a graphing calculator to graph the solution c)Compare results with part (a) Instructions

7. a)Sketch two possible solutions, one through the point ( -1, 3 ) 8.

8. b) Integrate to find the general solution

9. c) Graph solution using graphing calculator

10. Assignment Practice worksheet 6-1