2 Solutions for some nonlinear rational difference equations of dif- ferent orders: In the begining, we try to deduce the general solution for the following nonlinear rational generalized quadratic difference equations of order one in the form : Xn Xn+1 = (x₂)² + a where (ro)² + -a In order to do this we introduce the following notations: Let xo = a Consider the following notations: .In general we have A₁ = a² + a A₂ = a² + aA² A3 = a² A²+ aA² A₁ = a² A² A²+ a A² p-2 Ap =a²IIA² + αA²-1 i=1 where p > 3. ((1))

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Show me the steps of determine blue

2
Solutions for some nonlinear rational difference equations of dif-
ferent orders:
In the begining , we try to deduce the general solution for the following nonlinear rational generalized
quadratic difference equations of order one in the form :
Xn
Xn+1 =
(xn)² + a
where (xo)² + -a
In order to do this we introduce the following notations:
Let xo = a
Consider the following notations:
A1 = a? + a
A2 = a? + aA?
Az = a² A? + a A}
A4 = a² A{A? + aA?
.In general we have
р-2
Ap = a°I[4? + aA_1 where p 2 3.
((1))
p-1
i=1
Transcribed Image Text:2 Solutions for some nonlinear rational difference equations of dif- ferent orders: In the begining , we try to deduce the general solution for the following nonlinear rational generalized quadratic difference equations of order one in the form : Xn Xn+1 = (xn)² + a where (xo)² + -a In order to do this we introduce the following notations: Let xo = a Consider the following notations: A1 = a? + a A2 = a? + aA? Az = a² A? + a A} A4 = a² A{A? + aA? .In general we have р-2 Ap = a°I[4? + aA_1 where p 2 3. ((1)) p-1 i=1
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