Consider the system of equations And for the (non-zero) horizontal (y-)nullcline: y= 6(1-x) (Enter your equation, e.g., y=x.) (Note that there are also nullclines lying along the axes.) dx de = 2 (1-²-3) y) dt 5 taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=(5-x)/5 (Enter your equation, e.g., y=x.) (b) What are the equilibrium points for the system? Equilibria = (0,0), (5,0), (0,6), (25/29,24/29) (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).) dy = y(1-% -2), dt 6 (c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (4,1), trajectories converge to ✓the point (5/2, 1/2) (Enter the point as an (x,y) pair, e.g., (1,2).)
Consider the system of equations And for the (non-zero) horizontal (y-)nullcline: y= 6(1-x) (Enter your equation, e.g., y=x.) (Note that there are also nullclines lying along the axes.) dx de = 2 (1-²-3) y) dt 5 taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=(5-x)/5 (Enter your equation, e.g., y=x.) (b) What are the equilibrium points for the system? Equilibria = (0,0), (5,0), (0,6), (25/29,24/29) (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).) dy = y(1-% -2), dt 6 (c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (4,1), trajectories converge to ✓the point (5/2, 1/2) (Enter the point as an (x,y) pair, e.g., (1,2).)
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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please solve part c - other parts are correct
please solve it on paper
Transcribed Image Text:Consider the system of equations
And for the (non-zero) horizontal (y-)nullcline:
y= 6(1-x)
(Enter your equation, e.g., y=x.)
(Note that there are also nullclines lying along the axes.)
dx
dt
(b) What are the equilibrium points for the system?
Equilibria = (0,0), (5,0), (0,6), (25/29,24/29)
(Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).)
dy
dt
= x (1-3-y)
Y
y (1 - % - x),
6
taking (x, y) > 0.
(a) Write an equation for the (non-zero) vertical (x-)nullcline of this system:
y=(5-x)/5
(Enter your equation, e.g., y=x.)
= y
(c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence:
If we start at the initial position (4,1), trajectories converge to ✓the point (5/2, 1/2)
(Enter the point as an (x,y) pair, e.g., (1,2).)
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