Show that there is at least one solution in each of the second and fourth quadrants that tend to the origin as t goes to infinity.

Similarly, show that there is at least one solution in each of the first and third quadrants that tend to the origin as t goes to negative infinity.

No idea how I do this. Some help would be most appreciated!

Guess it would help if I posted the system :P

$\displaystyle dx/dt=y$

$\displaystyle dy/dt=x-x^2$