Consider the system of equations (see image) 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.)b. What are the equilibrium points for the system? (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 (3,1), trajectories [converge to, diverge from, cycle around, spiral into, spiral out from] the point (?, ?) Consider the system of equationsdx+ x(2 — х — Зу)dtdy— У(1 — 2х),dttaking (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 (3, 1), trajectories ?v the point(Enter the point as an (x,y) pair, e.g., (1,2).)

Answered: Image /qna-images/answer/f4200544-5589-47c8-9c20-ee51819c4b36.jpg

Consider the system of equations dx x(2 — х — Зу) dt dy = y(1 – 2x), dt 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 (3, 1), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)