Given the second-order difference equation. Yt+2-5Y₁+1 +6Y₁ = 2(5¹) + t (1) Write down the auxiliary equation: 2²² + M₁ = r+ (2) The roots of the auxiliary equation are and r₂ = OAr₁¹+ Br₂¹ OAr* + Btr¹ OAtr* + Btr¹ OAr+ Br OAr₁¹ + Btr₂¹ OAtr₁¹+ Btr₂² = 0 (3) The homogenous solution is of the form: Yh= (4) The particular solution is [use two decimal places where necessary] Yp = (55) + t +

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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Given the second-order difference equation.
Yt+2-5Y₁+1 +6Y₁ = 2(5¹) + t
(1) Write down the auxiliary equation:
2²² +
M₁ =
r+
(2) The roots of the auxiliary equation are
and r₂ =
OAr₁¹+ Br₂¹
OAr* + Btr¹
OAtr* + Btr¹
OAr+ Br
OAr₁¹ + Btr₂¹
OAtr₁¹+ Btr₂²
= 0
(3) The homogenous solution is of the form:
Yh=
(4) The particular solution is [use two decimal places where necessary]
Yp =
(55) +
t +
Transcribed Image Text:Given the second-order difference equation. Yt+2-5Y₁+1 +6Y₁ = 2(5¹) + t (1) Write down the auxiliary equation: 2²² + M₁ = r+ (2) The roots of the auxiliary equation are and r₂ = OAr₁¹+ Br₂¹ OAr* + Btr¹ OAtr* + Btr¹ OAr+ Br OAr₁¹ + Btr₂¹ OAtr₁¹+ Btr₂² = 0 (3) The homogenous solution is of the form: Yh= (4) The particular solution is [use two decimal places where necessary] Yp = (55) + t +
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