Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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