Show me the steps of deremine blue and inf is here i need evey I need all the details step by step and inf is here Motivated by the above studies, we study the dynamics of following higherorder difference equationXn+1 =A + B(2)where A, B are positive real numbers and the initial conditions are positivenumbers. Additionally, we investigate the boundedness, periodicity, oscillationbehaviours, global asymptotically stability and rate of convergence of relatedhigiorder difference equations.Consider the scalar kth-order linear difference equationx (n + k) + P1 (n)x (n + k – 1) + .+ Pk (n)x (n) = 0,(4)where k is a positive integer and p; : Z+ → C for i = 1,,k. Assume thatqi = lim p;(n), i = 1, ... , k,(5)exist in C. Consider the limiting equation of (4):x (n + k) + q1x (n + k – 1) ++ qkx (n) = 0.(6)Theorem 4 (Poincaré's Theorem) Consider (4) subject to condition (5).Let A1,, Ak be the roots of the characteristic equation入*+ 91入+ 9k(7)= 0..of the limiting equation (6) and suppose that |Ai| # |A;| for i # j. If x (n) isa solution of (4), then either x (n) = 0 for all large n or there exists an indexje {1,... , k} such thatx (n + 1)x (n)lim Theorem 5 Suppose that (5) holds. If x (n) is a solution of (4), then eitherx (n) := 0 eventually orlim sup (a; (n)|)/" = xj.where A1,, Ak are the (not necessarily distinct) roots of the characteristic..equation (7).Firstly, we take the change of the variables for Eq.(2) as follows ynFrom this, we obtain the following difference equationYnУп+1 — 1+Р-2Yn-mBwhere p = . From now on, we handle the difference equation (8). The uniquepositive equilibrium point of Eq.(8) isĄ² •1+ V1+4p

Given, equation xn+1=A+Bxnxn-m2 ...(2)

Answered: Yn Yn+1 = 1+P2 Yn-r

Yn Yn+1 = 1+P2 Yn-r

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

Similar questions

Hello, please answer all parts if possible. if not, please answer c, e and f, thank you.
answer completely please please, ill upvote
What type of rule is being used? Algebra, recíprocal, quotient, Pythagorean or odd/even?
Follow up please answer C,D ty!
Ps: AACT = TCAA so you divide by 2 for that case but AAAA and ACTCA are palindromes which you don't divide by 2
i need the answer quickly
the answer choices for the last question are 0 1/2 1 1/4 theres no 3/5