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Consider the system of equations dx dt = dx dt is a line on which dy dt x (5 - x - 6y) = y(1 - 5x), taking (x, y) > 0. Recall that a nullcline of this system is a line on which dy = dt = 0. Likewise, a vertical nullcline of this system t = 0, and a horizontal nullcline of this dy dx dt system is a line on which y = 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system:

Consider the system of equations dx dt = dx dt is a line on which dy dt x (5 - x - 6y) = y(1 - 5x), taking (x, y) > 0. Recall that a nullcline of this system is a line on which dy = dt = 0. Likewise, a vertical nullcline of this system t = 0, and a horizontal nullcline of this dy dx dt system is a line on which y = 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system:

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 dx dt dy dt x (5 – 5 - x - 6y) = y(1 – 5x), taking (x, y) > 0. Recall that a nullcline of this system is a line on which dx dy dt dt = 0. Likewise, a vertical nullcline of this system is a line on which t = 0, and a horizontal nullcline of this system is a line on which = 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 (6, 4), trajectories ? the point (Enter the point as an (x,y) pair, e.g., (1,2).)
Transcribed Image Text:Consider the system of equations dx dt dy dt x (5 – 5 - x - 6y) = y(1 – 5x), taking (x, y) > 0. Recall that a nullcline of this system is a line on which dx dy dt dt = 0. Likewise, a vertical nullcline of this system is a line on which t = 0, and a horizontal nullcline of this system is a line on which = 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 (6, 4), trajectories ? the point (Enter the point as an (x,y) pair, e.g., (1,2).)
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