This is the second part of a four-part problem. Let Wronskian det These functions are linearly independent to the system do [t²2t F₁(t) = [t - Compute the Wronskian to determine whether the functions ₁(t) and ₂(t) are linearly independent. 2t ÿ' = because the Wronskian is 21-2 -2t-2 32(t) = t [7¹]. nonzero ✓provided t = 0. Therefore, the solutions ₁(t) and 2(t) 12t ¹+2t-27 2t-¹-2-2 ✓ form a fundamental set (i.e., linearly independent set) of solutions. ý
This is the second part of a four-part problem. Let Wronskian det These functions are linearly independent to the system do [t²2t F₁(t) = [t - Compute the Wronskian to determine whether the functions ₁(t) and ₂(t) are linearly independent. 2t ÿ' = because the Wronskian is 21-2 -2t-2 32(t) = t [7¹]. nonzero ✓provided t = 0. Therefore, the solutions ₁(t) and 2(t) 12t ¹+2t-27 2t-¹-2-2 ✓ form a fundamental set (i.e., linearly independent set) of solutions. ý
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 second part of a four-part problem.
Let
ÿ₁(t)
Compute the Wronskian to determine whether the functions ÿ₁(t) and ÿ₂(t) are linearly independent.
Wronskian = det
do
2t
=
- [ ²³ 2 ²4], in(t) = [² 1 ¹].
2t
These functions are linearly independent ✓ because the Wronskian is nonzero
to the system
ÿ'
=
2t-2
2t
provided t = 0. Therefore, the solutions ÿ₁(t) and ÿ2(t)
12t-¹ + 2t-27
2t-¹-21-2
form a fundamental set (i.e., linearly independent set) of solutions.
15
ý](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05295cc1-71f0-4e3b-b6f8-2c1731c6d617%2F33e01c55-1b29-49d1-8f4e-4e16a12b5ac8%2Ftw3b5l8_processed.png&w=3840&q=75)
Transcribed Image Text:This is the second part of a four-part problem.
Let
ÿ₁(t)
Compute the Wronskian to determine whether the functions ÿ₁(t) and ÿ₂(t) are linearly independent.
Wronskian = det
do
2t
=
- [ ²³ 2 ²4], in(t) = [² 1 ¹].
2t
These functions are linearly independent ✓ because the Wronskian is nonzero
to the system
ÿ'
=
2t-2
2t
provided t = 0. Therefore, the solutions ÿ₁(t) and ÿ2(t)
12t-¹ + 2t-27
2t-¹-21-2
form a fundamental set (i.e., linearly independent set) of solutions.
15
ý
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