The trajectories curve and the direction with the eigenvalue largest in magnitude will approach zero fastest. All orbits lead away from the fixed point. The trajectories curve and the direction with the eigenvalue largest in magnitude will leave zero fastest. Stable in one direction, unstable in another. All trajectories lead to the fixed point and they spiral inward.
All trajectories lead away from the fixed point and they spiral outward.
All trajectories are closed orbits around the fixed point. Finally we discuss the case of degenrate roots where both eigenvalues are the same. In this case they have to be real or else we would have two more eigenvalues from the complex conjugates. In this case the solution of the DE takes the form and a term linear in time shows up. All trajectrories are straight lines into the fixed point.