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1. Indicate whether each of the following equations is linear or nonlinear. If linear, determine the solution; if nonlinear, find any steady states of the equa- tion. (a) Xn = (1 a)xn-1 + Bxn, a and 3 are constants (b) Xn+1 = 1 + xn (c) Xn+1=Xnean, a is a constant (Xn+1- a)² = (d) α²(x²/1 2x + 1), - a is a constant

1. Indicate whether each of the following equations is linear or nonlinear. If linear, determine the solution; if nonlinear, find any steady states of the equa- tion. (a) Xn = (1 a)xn-1 + Bxn, a and 3 are constants (b) Xn+1 = 1 + xn (c) Xn+1=Xnean, a is a constant (Xn+1- a)² = (d) α²(x²/1 2x + 1), - a is a constant

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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105.213. Redistribution subject- 1. Indicate whether each of the following equations is linear or nonlinear. If linear, determine the solution; if nonlinear, find any steady states of the equa- tion. (a) x₁ = (1 a and 3 are constants (b) Xn+1 = (c) Xn+1 = (d) (Xn+1 (e) Xn+1 = - a)xn-1 + Bxn, Xn 1 + xn Xn e-axn, a is a constant a)² = α²(x² - 2x + 1), a is a constant K k₁, k₂ and K are constants k₁ + k₂/xn'
Transcribed Image Text:105.213. Redistribution subject- 1. Indicate whether each of the following equations is linear or nonlinear. If linear, determine the solution; if nonlinear, find any steady states of the equa- tion. (a) x₁ = (1 a and 3 are constants (b) Xn+1 = (c) Xn+1 = (d) (Xn+1 (e) Xn+1 = - a)xn-1 + Bxn, Xn 1 + xn Xn e-axn, a is a constant a)² = α²(x² - 2x + 1), a is a constant K k₁, k₂ and K are constants k₁ + k₂/xn'
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