for a 2nd order DE

find critical pts from the DE... i.e. where dy/dx = 0 or undefined

draw a vertical line representing the y-axis, this will be the phase line

indicate the positions of the critical points (constant/equilibrium solutions, so draw horizontal lines at those points) on the phase line

notice this will divide the line into regions

use (d^2)y/d(x^2) to determine the sign of the solution y(x) in those regions

put an ^ symbol on the phase line if the sign of that region determined from the 2nd deriv is positive, and an upsidedown ^ if the sign of that region is negative

the dots represent your critical points on the line, tilt your head sideways > . < asymptotically stable, < . < or > . > semistable, < . > asymptotically unstable (referring to the stability of that point)

the stability of these points may also be identified by classifying those points as attractors (stable) or repellers (unstable)