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(Difference equations.) Consider the second-order difference equation max{1, xn} X'n+1 = n = 0,1, 2, . .. Xn-1 (a) Given the initial conditions x-1 = 5 and xo = 4, find the first 12 terms of the solution {xn}.

(Difference equations.) Consider the second-order difference equation max{1, xn} X'n+1 = n = 0,1, 2, . .. Xn-1 (a) Given the initial conditions x-1 = 5 and xo = 4, find the first 12 terms of the solution {xn}.

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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(Difference equations.) Consider the second-order difference equation max{1, xn} Xn+1 n = 0, 1, 2, ... Xn-1 (a) Given the initial conditions x_1 = 5 and xo = 4, find the first 12 terms of the solution {xn}. (b) Choose your own positive numbers for initial conditions for this difference equation, and calcu- late its first few terms given your chosen initial conditions. Then, make a conjecture about the behaviour of all positive solutions of this difference equation. (You do not need to prove that this conjecture is true!)
Transcribed Image Text:(Difference equations.) Consider the second-order difference equation max{1, xn} Xn+1 n = 0, 1, 2, ... Xn-1 (a) Given the initial conditions x_1 = 5 and xo = 4, find the first 12 terms of the solution {xn}. (b) Choose your own positive numbers for initial conditions for this difference equation, and calcu- late its first few terms given your chosen initial conditions. Then, make a conjecture about the behaviour of all positive solutions of this difference equation. (You do not need to prove that this conjecture is true!)
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