dx/dt = ax + y

dy/dt = x²/(1 + x²) by

Show that if 2ab > 1 there is only one fixed point at the origin and that if 2ab < 1 there are two more fixed points, x,1 and x,2 with 0 < x,1 < x,2.

State x,1 and x,2 in terms of a and b.

Make a qualitative phase plot for 2ab < 1 by sketching the nullclines and penciling in the direction of the vector field in the resulting 4 regions of the first quadrant.