Consider the system of linear ODES The system of equation written as y' (t) = Ay(t), where y(t) = ₂(t) 93 (t)) (a) Enter the matrix A in the box below. sin (a) 91 (t)=33 y₁ (t)-9 32 (t) + 25 y3 (t). 92 (t)=38 y₁ (t)- 14 y2 (t) + 25 y3 (t). d 3 (t)=-20 y₁ (t)- 21 y3 (t). (v₁ (t)) dz v₁ (t)= 4 Ae-5t-5 Belt +Ce-t 12(t)= v3(t)= f (b) Given that the matrix A has eigenvectors 3 0·00 with respective eigenvalues -5,4,-1. Enter the solution of 32(t) and 33 (t) in Maple syntax, making sure the answer is consistent with the given form of 1 8 60 a Ω

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the system of linear ODES
(3₁ (t))
The system of equation written as y' (t) = Ay(t), where y(t) = 12 (1)
93 (t)
(a) Enter the matrix A in the box below.
sin (a)
8
dr
v₁ (t)= 4 Ae-5t-5 Belt +Ce-t
1/2 (t)=
v3 (t).
91 (t)=33 y₁ (t)-9 y2 (t) + 25 y/3 (t).
92 (t)=38 y₁ (t)-14 y2 (t) + 25 y3 (t).
3 (t)=-20 y1 (t)-21 yz (t).
f
(b) Given that the matrix A has eigenvectors 3
20
60
8
000
with respective eigenvalues -5,4,-1.
Enter the solution of 32(t) and 33 (t) in Maple syntax, making sure the answer is consistent with the given form of y₁ (t).
a Ω
E
Transcribed Image Text:Consider the system of linear ODES (3₁ (t)) The system of equation written as y' (t) = Ay(t), where y(t) = 12 (1) 93 (t) (a) Enter the matrix A in the box below. sin (a) 8 dr v₁ (t)= 4 Ae-5t-5 Belt +Ce-t 1/2 (t)= v3 (t). 91 (t)=33 y₁ (t)-9 y2 (t) + 25 y/3 (t). 92 (t)=38 y₁ (t)-14 y2 (t) + 25 y3 (t). 3 (t)=-20 y1 (t)-21 yz (t). f (b) Given that the matrix A has eigenvectors 3 20 60 8 000 with respective eigenvalues -5,4,-1. Enter the solution of 32(t) and 33 (t) in Maple syntax, making sure the answer is consistent with the given form of y₁ (t). a Ω E
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