How to draw phase portraits by hand effectively?

[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.