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Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y =sint cos t, y2 = 5 sin 2t

Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y =sint cos t, y2 = 5 sin 2t

Advanced Engineering Mathematics
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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Question
Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y1 =sint cos t, y, = 5 sin 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = y, on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) O B. Since y, =O2 on (0,1), the functions are linearly independent on (0,1) (Simplify your answer.) O C. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0,1). O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0,1).
Transcribed Image Text:Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y1 =sint cos t, y, = 5 sin 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = y, on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) O B. Since y, =O2 on (0,1), the functions are linearly independent on (0,1) (Simplify your answer.) O C. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0,1). O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0,1).
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