1. Differential Equations and Slope Fields 6.1

2. Differential Equations  An equation involving a derivative is called a differential equation.  The order of the differential equation is determined by the highest ordered derivative.

3. Examples  Determine the order:

4. Solving Differential Eq.

5. Initial Value  Find the particular solution to the equation whose graph passes through the point (1,0) passes through the point (1,0)

6. Slope Fields  A diagram depicting the slopes of a differential equation at different points. Gives you an idea of what the graph should look like.

7. Example  Construct a slope field for  Sketch the particular solution through (0,2).

8. Example (implicitly defined)  Construct a slope field for the equation

9. Homework  Pg 327 #12, 15, 18-20, 26-34 even, 58