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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 =

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 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
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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