Consider the system of equations $$\frac{dx}{dt} = x\left(1-\frac{x}{2}-y\right)$$ $$\frac{dy}{dt} = y\left(1-\frac{y}{3}-x\right),$$ taking $(x,y) > 0$.

(a) Write an equation for the (non-zero) vertical ($x$-)nullcline of this system:

(Enter your equation, e.g., y=x.)

And for the (non-zero) horizontal ($y$-)nullcline:

(Enter your equation, e.g., y=x.)
(Note that there are also nullclines lying along the axes.)

(b) What are the equilibrium points for the system?
Equilibria =
(Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).)

(c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence:
If we start at the initial position $(\frac{3}{2},\frac{1}{2})$, trajectories ? converge to diverge from cycle around spiral into spiral out from the point .
(Enter the point as an (x,y) pair, e.g., (1,2).)