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How to draw phase portraits by hand effectively?

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Qingyang Wei:
The only method of drawing phase portrait that I am aware of is to evaluate each particular solutions of the system at a large amount of points, and "connect the dots" to produce a trajectory for the solution. But that seems to be very time consuming. Is there any more efficient way to draw this by hand?

Karim El Komaishy:
Try finding the eigenvectors as well as the eigenvalues as the eigenvectors can tell you the direction of the trajectories

Ruowen Xia:
You can divided into different situations, like 2 distinct real roots, 2 same real roots and non-real roots. and fine the corresponding eigenvector, and first draw these eigenvectors

Zhihao Zuo:
I got the same question. And sometimes I just couldn't connect all the lines together however hard I try.

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