[2] 5. Consider the system: da dt dy dt = x(10-x-y) = y(30 - 2r - y) (a) (To, yo) (5, 10) = x(t) →. y(t) → as t → ∞ 40 as t → ∞ 30 +x 40 10 20 30 A phase portrait for this system is given to the right of the system. On the phase portrait, the z and y nullclines are provided along with various vectors on the corresponding vector field. Using this information, determine the long term behavior of a solution with the given initial condition. (Fill in the blank) 20- 10% (b) (zo, yo)=(5,0.1) x(t) → y(t) →. as t → ∞ as t → ∞
[2] 5. Consider the system: da dt dy dt = x(10-x-y) = y(30 - 2r - y) (a) (To, yo) (5, 10) = x(t) →. y(t) → as t → ∞ 40 as t → ∞ 30 +x 40 10 20 30 A phase portrait for this system is given to the right of the system. On the phase portrait, the z and y nullclines are provided along with various vectors on the corresponding vector field. Using this information, determine the long term behavior of a solution with the given initial condition. (Fill in the blank) 20- 10% (b) (zo, yo)=(5,0.1) x(t) → y(t) →. as t → ∞ as t → ∞
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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Question
![[2] 5. Consider the system:
da
dt
dy
dt
= x(10- x - y)
= y(30-2r - y)
(a) (To, yo) (5, 10)
=
x(t) →
y(t) →
40-
as t → ∞
as t → ∞
30
20
10
20
30
40
A phase portrait for this system is given to the right of the system. On the phase portrait, the
z and y nullclines are provided along with various vectors on the corresponding vector field.
Using this information, determine the long term behavior of a solution with the given initial
condition. (Fill in the blank)
10
(b) (ro, 30) = (5,0.1)
x(t) →
y(t) →
as t → ∞
as t→∞](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00e5c5de-298c-41fb-9861-0262471f9c17%2F40892157-360e-4766-b598-e8f4e00e0084%2Fld9ruef_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[2] 5. Consider the system:
da
dt
dy
dt
= x(10- x - y)
= y(30-2r - y)
(a) (To, yo) (5, 10)
=
x(t) →
y(t) →
40-
as t → ∞
as t → ∞
30
20
10
20
30
40
A phase portrait for this system is given to the right of the system. On the phase portrait, the
z and y nullclines are provided along with various vectors on the corresponding vector field.
Using this information, determine the long term behavior of a solution with the given initial
condition. (Fill in the blank)
10
(b) (ro, 30) = (5,0.1)
x(t) →
y(t) →
as t → ∞
as t→∞
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