Find all equilibrium solutions of the equation dydx y2 1 U

Find all equilibrium solutions of the equation dy/dx = y^2 - 1. Use only qualitative analysis to sketch the graphs of solutions having various representative initial values y(0).

Solution

Equilibrium solutions are given by dy/dt=0

so y²-1=0

(y+1)(y-1)=0

y=-1,y=1

tharefore y=-1,y=1 are equilibrium solutions