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(1 point) Consider the system of equations dx = X dt (1-) 5 dy = y ( 1 dt -x). y 6 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 (4, ;), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)

(1 point) Consider the system of equations dx = X dt (1-) 5 dy = y ( 1 dt -x). y 6 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 (4, ;), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 (4,1/2), trajectories [converge to, diverge from, cycle around, spiral into, spiral out from] the point (?, ?)

(1 point) Consider the system of equations *=-(1--) >(1 -{ -x). dx = X dt - V dy = y 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 (4, -), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)
Transcribed Image Text:(1 point) Consider the system of equations *=-(1--) >(1 -{ -x). dx = X dt - V dy = y 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 (4, -), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)
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