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Consider the recursive relation 9xt Xt+1 = C 1+ xt

Consider the recursive relation 9xt Xt+1 = C 1+ xt

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 recursive relation 9xt X++1 = c 1+ ¤t where c > 0 is an unknown constant. (a) Find all equilibrium points. Answer: x = 0 and x = -1+9*c Your last answer was interpreted as follows: Your last answer was interpreted as follows: -1+9. c (b) For which values of c is the zero equilibrium stable and the other one unstable? Answer: c < : (c) For which values of c is the zero equilibrium unstable and the other one stable? Answer: c < + (d) Let us call c* the critical value that distinguishes the two cases above. What is the value of c* ? Answer: c* (e) In the case of c = c*, we cannot say anything about the stability since |f'(7)| =
Transcribed Image Text:Consider the recursive relation 9xt X++1 = c 1+ ¤t where c > 0 is an unknown constant. (a) Find all equilibrium points. Answer: x = 0 and x = -1+9*c Your last answer was interpreted as follows: Your last answer was interpreted as follows: -1+9. c (b) For which values of c is the zero equilibrium stable and the other one unstable? Answer: c < : (c) For which values of c is the zero equilibrium unstable and the other one stable? Answer: c < + (d) Let us call c* the critical value that distinguishes the two cases above. What is the value of c* ? Answer: c* (e) In the case of c = c*, we cannot say anything about the stability since |f'(7)| =
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