[ 2t ute the Wronskian to determine whether the functions y, (t) and y2(t) are linearly independent. Wronskian = det functions are linearly independent v because the Wronskian is nonzero v provided t 7
[ 2t ute the Wronskian to determine whether the functions y, (t) and y2(t) are linearly independent. Wronskian = det functions are linearly independent v because the Wronskian is nonzero v provided t 7
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
![Let
2 – 2t
vi(t) = ||
-
½(t) :
2t
Compute the Wronskian to determine whether the functions y1(t) and y2(t) are linearly independent.
Wronskian = det
=
These functions are linearly independent
v because the Wronskian is
v provided t 0. Therefore, the solutions y1 (t) and y2(t) to the
nonzero
system
2t-2
1- 21-1 + 21-2
-21-2
2t-1 – 21-2
do
form a fundamental set (i.e., linearly independent set) of solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2eee5fef-24c0-42d2-a99f-ec7ca4df2e97%2F3996206b-1025-4ecd-bd8d-af2983e7b79a%2Fy2ojkvr_processed.png&w=3840&q=75)
Transcribed Image Text:Let
2 – 2t
vi(t) = ||
-
½(t) :
2t
Compute the Wronskian to determine whether the functions y1(t) and y2(t) are linearly independent.
Wronskian = det
=
These functions are linearly independent
v because the Wronskian is
v provided t 0. Therefore, the solutions y1 (t) and y2(t) to the
nonzero
system
2t-2
1- 21-1 + 21-2
-21-2
2t-1 – 21-2
do
form a fundamental set (i.e., linearly independent set) of solutions.
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