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This animation helps visualize phase planes for the case of two real eigenvalues.

We start with the two eigendirections (blue, where straight-line solutions live) orthogonal to each other (the x-axis corresponds to the eigenvalue with smallest absolute value, the y-axis the other one).
Then, we rotate the second eigenvector (the first one remains on the x-axis).
The red curves represent 4 typical trajectories.
You may run the animation at three speeds (click as desired, and click start/stop), or you may step through the pictures one at a time.


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