Today, we’ll consider differential equations with two variables.
Linear
There are a couple different shapes that 2D systems can take on:
| type | image | eigenvalues? |
|---|---|---|
| spiral |  | complex conjugates |
| center |  | conjugates + purely imaginary |
| node |  | same sign |
| saddle |  | different sign |
The node and spiral shown are unstable (i.e. radiating away from the origin); reversing the direction of the arrows would make them stable.