Consider the autonomous system x'(t) = sin(x) - cos(x). Which of the followin statements are true? (1) All solutions ä(t) are defined for all t. (2) There are solutions (t) such that limt→+∞ x(t) = +∞0. (3) The equilibrium values for x are + nπ, where n = 0, ±1, ±2, ±3, . . .. (4) All equilibrium values are unstable. ㅠ + nπ is stable if and only if n is odd. (5) x ○ (1), (2), (3), (4) are true. (5) is false. ○ (1), (3), (5) are true. (2) are (4) are false. ○ (1), (2), (3), (5) are true. (4) is false. O (2) and (3) are true. (1), (4), (5) are false. None of (a), (b), (c), (d) describes the situation =
Consider the autonomous system x'(t) = sin(x) - cos(x). Which of the followin statements are true? (1) All solutions ä(t) are defined for all t. (2) There are solutions (t) such that limt→+∞ x(t) = +∞0. (3) The equilibrium values for x are + nπ, where n = 0, ±1, ±2, ±3, . . .. (4) All equilibrium values are unstable. ㅠ + nπ is stable if and only if n is odd. (5) x ○ (1), (2), (3), (4) are true. (5) is false. ○ (1), (3), (5) are true. (2) are (4) are false. ○ (1), (2), (3), (5) are true. (4) is false. O (2) and (3) are true. (1), (4), (5) are false. None of (a), (b), (c), (d) describes the situation =
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Question
![Consider the autonomous system x' (t)
statements are true?
=
sin(x) — cos(x). Which of the following
(1) All solutions ä(t) are defined for all t.
(2) There are solutions (t) such that limƉ→+∞ ä(t)
X
= +∞.
ㅠ
(3) The equilibrium values for î are + nÃ, where n = 0, ±1, ±2, ±3, . . ..
(4) All equilibrium values are unstable.
(5) x = + nπ is stable if and only if n is odd.
O (1), (2), (3), (4) are true. (5) is false.
○ (1), (3), (5) are true. (2) are (4) are false.
O (1), (2), (3), (5) are true. (4) is false.
O (2) and (3) are true. (1), (4), (5) are false.
O None of (a), (b), (c), (d) describes the situation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36ab9b77-502c-40e9-b186-8d956cf356fa%2Fe89dd118-8d6f-42bd-bc05-e4736d692202%2F384igul_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the autonomous system x' (t)
statements are true?
=
sin(x) — cos(x). Which of the following
(1) All solutions ä(t) are defined for all t.
(2) There are solutions (t) such that limƉ→+∞ ä(t)
X
= +∞.
ㅠ
(3) The equilibrium values for î are + nÃ, where n = 0, ±1, ±2, ±3, . . ..
(4) All equilibrium values are unstable.
(5) x = + nπ is stable if and only if n is odd.
O (1), (2), (3), (4) are true. (5) is false.
○ (1), (3), (5) are true. (2) are (4) are false.
O (1), (2), (3), (5) are true. (4) is false.
O (2) and (3) are true. (1), (4), (5) are false.
O None of (a), (b), (c), (d) describes the situation
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