What do you read from all those lines in a direction field?

Question

And what is an equilibrium solution.

Answer 1

You get the displacement in phase-space. An equilibrium solution is just what the name implies: a closed circuit in the phase-space of the problem which is stable and neither grows nor decays.


Doug

Answer 2

The direction field tells you where the system tends to go when it starts off at a given point. They are the tangents to the orbit. An equilibrium solution is one for which the orbit is closed. A stable orbit has nearby arrows pointing back toward the orbit--so if the system is displaced from it, it returns to the "stable" state. A stable/unstable equilibrium point is one for which the arrows all point toward/away from it (locally). At an equilibrium point itself there is no arrow (just like in regular calculus--the first derivative vanishes in all directions).

Answer 3

Why not try doing your own homework for a change. The forum is not meant to improve your grades. Read the text and do the work!