2.22. Plot the curve Yk+1 = y% – 2yk + 2 and analyze the stability of any fixed points. Show that the exact solution to this equation is Yk = 1+ c2", c= constant. Determine the interval of initial values of yk that correspond, respec- tively, to |c| > 1 and |c| < 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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2.22. Plot the curve
Yk+1 = Yk – 2yk +2
and analyze the stability of any fixed points. Show that the exact
solution to this equation is
Yk = 1+ c2*.
c = constant.
Determine the interval of initial values of yk that correspond, respec-
tively, to |c| > 1 and |c| < 1.
Transcribed Image Text:2.22. Plot the curve Yk+1 = Yk – 2yk +2 and analyze the stability of any fixed points. Show that the exact solution to this equation is Yk = 1+ c2*. c = constant. Determine the interval of initial values of yk that correspond, respec- tively, to |c| > 1 and |c| < 1.
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