This is the first part of a two-part problem. Let 3₁ (t) = [ P- [43]. cos(4t) -sin(4t) a. Show that y₁ (t) is a solution to the system ÿ' product ÿ{(t) = ÿ₂ (t) = Enter your answers in terms of the variable t. -4 sin(4t) -4 cos(4t)] 04 [](1) -4 = Pý by evaluating derivatives and the matrix 181-18 [8] Enter your answers in terms of the variable t. b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product 04 ÿ2(t) = [_4_1|ÿ2(t) [181-18]
This is the first part of a two-part problem. Let 3₁ (t) = [ P- [43]. cos(4t) -sin(4t) a. Show that y₁ (t) is a solution to the system ÿ' product ÿ{(t) = ÿ₂ (t) = Enter your answers in terms of the variable t. -4 sin(4t) -4 cos(4t)] 04 [](1) -4 = Pý by evaluating derivatives and the matrix 181-18 [8] Enter your answers in terms of the variable t. b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product 04 ÿ2(t) = [_4_1|ÿ2(t) [181-18]
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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![This is the first part of a two-part problem.
Let
P=[-: 1
5₁(t) = [(41) 5₂(t) =
- sin(4t).
a. Show that y₁ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix
product
y(t) =
=
0
[1]
-4
Enter your answers in terms of the variable t.
-4 sin(4t)
-4 cos(4t)]
ÿ₁ (t)
[181-18]
b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix
product
Enter your answers in terms of the variable t.
04]
32(t) = [-28]|2(t)
181-181](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3f1eaed-a98f-4503-b42a-126d8424ff90%2Fcec7b8a9-14c3-4a06-bcf0-050d2d9df67d%2Flhntys_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This is the first part of a two-part problem.
Let
P=[-: 1
5₁(t) = [(41) 5₂(t) =
- sin(4t).
a. Show that y₁ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix
product
y(t) =
=
0
[1]
-4
Enter your answers in terms of the variable t.
-4 sin(4t)
-4 cos(4t)]
ÿ₁ (t)
[181-18]
b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix
product
Enter your answers in terms of the variable t.
04]
32(t) = [-28]|2(t)
181-181
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