AJSesinando
Analyzing Autonomous Equations Using Phase Lines in Differential Equations
A phase line is a quick way to see where the solutions of an autonomous equation end up over a long time, without solving the equation. An autonomous equation is one where the right-hand side depends only on x, not on time. You find the critical points, where x dot is zero, check whether x dot is positive or negative between them, and read off whether each critical point is stable or unstable.