We know that for the non-linear system the differential equation is

dx/dt=y

dy/dt=-x+x^3 -y

the equilibrium point are (0,0),(1,0),and (-1,0)

the linerized system at (0,0) is dx/dt=y, dy/dt=-x-y

the linerized system at (1,0) is dx/dt=y, dy/dt=2x-y

the linerized system at (-1,0) is dx/dt=y, dy/dt=2x-y

For each of the linearized systems you found, determine the general solution, draw the corresponding phase portrait, and classify it.