3) This is the first part of a two-part problem. Let P = 7₁ (t) = [_(f cos(2t) (sin(2t)) 72(t) = 72 (t) = -2 sin(2t) -2 cos(2t). a. Show that ₁ (t) is a solution to the system y' = Py by evaluating derivatives and the matrix product 02 í (t) = - [ 2 ] 1 (1) Enter your answers in terms of the variable t. b. Show that ₂ (t) is a solution to the system y' = Py by evaluating derivatives and the matrix product 72(t) = [_23 [232(0) 72 (t) -2 Enter your answers in terms of the variable t. [23]
3) This is the first part of a two-part problem. Let P = 7₁ (t) = [_(f cos(2t) (sin(2t)) 72(t) = 72 (t) = -2 sin(2t) -2 cos(2t). a. Show that ₁ (t) is a solution to the system y' = Py by evaluating derivatives and the matrix product 02 í (t) = - [ 2 ] 1 (1) Enter your answers in terms of the variable t. b. Show that ₂ (t) is a solution to the system y' = Py by evaluating derivatives and the matrix product 72(t) = [_23 [232(0) 72 (t) -2 Enter your answers in terms of the variable t. [23]
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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#3
![3) This is the first part of a two-part problem.
Let
P=
7₁ (t) = [_(off
cos(2t)
(sin(2t))
72(t) =
72 (t) =
-2 sin(2t)
-2 cos(2t)
a. Show that ₁ (t) is a solution to the system y' = Pÿ by evaluating derivatives and the matrix product
J1 (t)
=
- [23] 1 (1)
Enter your answers in terms of the variable t.
b. Show that ₂ (t) is a solution to the system y' = Py by evaluating derivatives and the matrix product
02
72 (t) = [_23 72 (t)
-2 0
Enter your answers in terms of the variable t.
[23]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03fb929a-cbd9-4645-8c09-6942d746fc16%2Fce6ad8a7-3934-49c8-9df7-b8674e533c7b%2F8hqjl0c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3) This is the first part of a two-part problem.
Let
P=
7₁ (t) = [_(off
cos(2t)
(sin(2t))
72(t) =
72 (t) =
-2 sin(2t)
-2 cos(2t)
a. Show that ₁ (t) is a solution to the system y' = Pÿ by evaluating derivatives and the matrix product
J1 (t)
=
- [23] 1 (1)
Enter your answers in terms of the variable t.
b. Show that ₂ (t) is a solution to the system y' = Py by evaluating derivatives and the matrix product
02
72 (t) = [_23 72 (t)
-2 0
Enter your answers in terms of the variable t.
[23]
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