Given the second-order difference equation. Yt+2-7Yt+1 + 10Y₁ = 4t + 8t (1) Write down the auxiliary equation: r₁ = r+ (2) The roots of the auxiliary equation are and r₂ = = 0 OAr₁¹+ Br₂t OArt + Btrt OAtrt + Btrt OArt + Brt OAr₁¹+ Btr₂t OAtr₁¹ + Btr₂t (3) The homogenous solution is of the form: Yn = (4) The particular solution is [use two decimal places where necessary]
Given the second-order difference equation. Yt+2-7Yt+1 + 10Y₁ = 4t + 8t (1) Write down the auxiliary equation: r₁ = r+ (2) The roots of the auxiliary equation are and r₂ = = 0 OAr₁¹+ Br₂t OArt + Btrt OAtrt + Btrt OArt + Brt OAr₁¹+ Btr₂t OAtr₁¹ + Btr₂t (3) The homogenous solution is of the form: Yn = (4) The particular solution is [use two decimal places where necessary]
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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Provide answers for the following.
![Given the second-order difference equation.
Yt+2-7Yt+1 + 10Y₁ = 4t + 8t
(1) Write down the auxiliary equation:
r₁ =
r+
(2) The roots of the auxiliary equation are
and r₂ =
OAr₁¹+ Br₂t
OArt + Btrt
OAtrt + Btrt
OArt + Brt
OAr₁¹+ Btr₂t
OAtr₁¹ + Btr₂t
= 0
(3) The homogenous solution is of the form:
Yn =
(4) The particular solution is [use two decimal places where necessary]
Yp =
(4¹) +
t +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36abb20b-0a2e-4f12-9cbc-603849c615ac%2F4e9f4883-67c3-4bb8-bf33-d4ff2566b242%2Fu1nye2_processed.png&w=3840&q=75)
Transcribed Image Text:Given the second-order difference equation.
Yt+2-7Yt+1 + 10Y₁ = 4t + 8t
(1) Write down the auxiliary equation:
r₁ =
r+
(2) The roots of the auxiliary equation are
and r₂ =
OAr₁¹+ Br₂t
OArt + Btrt
OAtrt + Btrt
OArt + Brt
OAr₁¹+ Btr₂t
OAtr₁¹ + Btr₂t
= 0
(3) The homogenous solution is of the form:
Yn =
(4) The particular solution is [use two decimal places where necessary]
Yp =
(4¹) +
t +
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