1. 1 6.1 Slope Fields and Euler's Method Objective: Solve differential equations graphically and numerically.

2. 2 Slope Fields: a graphical approach Solving some DEs can be difficult or even impossible  Take a graphical approach Consider y’= F ( x, y )  At each point (x, y) in the xy-plane where F is defined, the DE determines the slope y’= F ( x, y ) of the solution at that point.  If you draw a short line segment with slope F ( x, y ) at selected points (x, y) in the domain of F, these line segments form a slope field.  A slope field shows the general shape of all the solutions

3. 3 Sketch the slope field for the differential equation y’= x - y

4. 4

5. 5 Match the slope field to the DE

6. 6 Sketch the slope field for the differential equation y’= 2x + y Use your slope field to sketch the solution that passes through (1,1)

7. 7 Sketch the slope field for the differential equation y’= 2x + y Use your slope field to sketch the solution that passes through (1,1)