7- Write the differential equation y"(t) - 2y"(t)- y'(t) + 3y(t) = 0 as a first order system. [x' (t)] 0 0 a) (t) (t) (t)] b) x₂(t) [(t) (t)] = 1 0 (t) JE x₂(t) [x3(t). [x₁(t) x₂ (t) [x3(1)] 01 - -3 1 2 [0 2 0 00-3 1 0 1 [0 1 0] [1(t) 0 0 1 1-3 -3 16 2] 2 3(t). x₁ (t)] x₂(t) [x3(1)] c)₂(t) (t) [a(t)] [0 1 0 d) (t) = 001 96 [x' (t)] [x (t)] Го 1 0 x(t) 00 2 1-3 x₂(t) DE 1 1 2 3 3 (t)]
7- Write the differential equation y"(t) - 2y"(t)- y'(t) + 3y(t) = 0 as a first order system. [x' (t)] 0 0 a) (t) (t) (t)] b) x₂(t) [(t) (t)] = 1 0 (t) JE x₂(t) [x3(t). [x₁(t) x₂ (t) [x3(1)] 01 - -3 1 2 [0 2 0 00-3 1 0 1 [0 1 0] [1(t) 0 0 1 1-3 -3 16 2] 2 3(t). x₁ (t)] x₂(t) [x3(1)] c)₂(t) (t) [a(t)] [0 1 0 d) (t) = 001 96 [x' (t)] [x (t)] Го 1 0 x(t) 00 2 1-3 x₂(t) DE 1 1 2 3 3 (t)]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![7- Write the differential equation y"(t) - 2y"(t)- y'(t) + 3y(t) = 0 as a first order system.
[x' (t)] 0
0
a) (t)
(t)
(t)]
b) x₂(t)
(t)
(t)]
=
1 0] [1(t)
JE
01
-3 1 2
-
[0 2 0
00-3
1 0 1
c) x₂(t) = 001
(t)
[a(t)]
[0 1 0
d) (t) = 001
x₂ (t)
[x3(1)]
[0 1 0] [1(t)]
x₂(t)
-3 2 3(t).
16
2 1-3
[a(t)] [0 1 0
x(t)
00
x₂(t)
x3(t).
96
₁ (t)]
1 2 3
x₂(t)
[x3(1)]
96
1
3 (t)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8850039d-812e-4971-8e5d-db8c81fde42b%2F7aaa6a40-e557-46f7-9446-07421f37a2e8%2Ff7ku1sn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7- Write the differential equation y"(t) - 2y"(t)- y'(t) + 3y(t) = 0 as a first order system.
[x' (t)] 0
0
a) (t)
(t)
(t)]
b) x₂(t)
(t)
(t)]
=
1 0] [1(t)
JE
01
-3 1 2
-
[0 2 0
00-3
1 0 1
c) x₂(t) = 001
(t)
[a(t)]
[0 1 0
d) (t) = 001
x₂ (t)
[x3(1)]
[0 1 0] [1(t)]
x₂(t)
-3 2 3(t).
16
2 1-3
[a(t)] [0 1 0
x(t)
00
x₂(t)
x3(t).
96
₁ (t)]
1 2 3
x₂(t)
[x3(1)]
96
1
3 (t)]
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