This is the second part of a two-part problem. Let 3,0) - [- cos(2t) -2 sin(2t) (t) = (sin(2t))] I2(t) = -2 cos(2t) Compute the Wronskian to determine whether the functions j, (t) and j2 (t) are linearly independent. Wronskian = det These functions are linearly Choose because the Wronskian is Choose for all t. Therefore, the solutions j, (t) and j, (t) to the system Choose 0 2 dependent independent Choose v form a fundamental set (i.e., linearly independent set) of solutions.
This is the second part of a two-part problem. Let 3,0) - [- cos(2t) -2 sin(2t) (t) = (sin(2t))] I2(t) = -2 cos(2t) Compute the Wronskian to determine whether the functions j, (t) and j2 (t) are linearly independent. Wronskian = det These functions are linearly Choose because the Wronskian is Choose for all t. Therefore, the solutions j, (t) and j, (t) to the system Choose 0 2 dependent independent Choose v form a fundamental set (i.e., linearly independent set) of solutions.
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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Show all the steps and Complete the sentence:
These functions are linearly (dependent/independent) because the Wronskian is (zero/non-zero) for all tt.
(Do/Do not) form a fundamental set (i.e., linearly independent set) of solutions.
![This is the second part of a two-part problem.
Let
cos(2t)
-2 sin(2t)
ÿ, (t) =
I2(t) =
(sin(2t))]
-2 cos(2t)
Compute the Wronskian to determine whether the functions j, (t) and j2 (t) are linearly independent.
Wronskian = det
These functions are linearly Choose
because the Wronskian is Choose
for all t. Therefore, the solutions j, (t) and j, (t) to the system
Choose
0 2
dependent
independent
Choose v form a fundamental set (i.e., linearly independent set) of solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6da5ff5-4f9e-46f1-b6af-425e0be2530f%2F92fd1945-31ce-4fd4-a8ca-02889c93b15a%2Flxmhsek_processed.png&w=3840&q=75)
Transcribed Image Text:This is the second part of a two-part problem.
Let
cos(2t)
-2 sin(2t)
ÿ, (t) =
I2(t) =
(sin(2t))]
-2 cos(2t)
Compute the Wronskian to determine whether the functions j, (t) and j2 (t) are linearly independent.
Wronskian = det
These functions are linearly Choose
because the Wronskian is Choose
for all t. Therefore, the solutions j, (t) and j, (t) to the system
Choose
0 2
dependent
independent
Choose v form a fundamental set (i.e., linearly independent set) of solutions.
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