Slope Fields Slope Fields

Introduction

We can graph possible solutions to differential equations with slope fields.

Slope fields are graphed by drawing tangent lines to possible solutions at many points.

\frac{dy}{dx}=x+y
Slope fields allow us to see what possible solution functions look like.

The solution to
\frac{dy}{dx}=x+y
is
y=-x-1+ke^x
It is graphed below
5
times, with
5
different constants.
Here is the same graph with a denser slope field, so it is easier to see the how the lines are tangent to the solution functions.

Examples

Here are some more examples of differential equations and their slope fields.

Click on the graphs to see possible solution functions.

\frac{dy}{dx}=x-y
\frac{dy}{dx}=x
\frac{dy}{dx}=2