9.2 Direction/Slope Fields

Direction/Slope Fields!!!!

Direction fields are a way to approximate the solution of the differential equation graphically. (But it is extremely imprecise.)
(Remember, differential equations are equations with the derivative of the function and the function itself.)

It is easiest to learn through an example so....

Given the differential equation y’ = 2x + y, sketch the graph of the equation going through the origin.

1) It is important to remember that slope fields are an extremely imprecise way to find the solution. The first step of solving a problem is to make a chart.

X Y Y’
0 0 0
0 1 1
1 1 3
.
.
.
and so on and so forth. Etc etc.

At each point, draw a small line with the calculated slope until you have a graph something like this....
2) Since the problem is asking for the graph through the origin, so start at the origin and following the slope lines until a graph forms.



This is an extra link to help you! http://www.sosmath.com/diffeq/slope/slope1.html

http://kme.truman.edu/images/difeq.jpg
:) It’s...cute.

TAYLOR YOU’RE UP NEXT.