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a) Functions y1, y2,., Yn are said to be linearly independent on an interval I if the equation c1y1 + c2y2 + +CnYn = 0 has only a trivial solution, namely c = c2 = .. = Cn = 0 on I. By using the definition, determine whether or not y1 = sin 3x and y2 = cos 3x are linearly independent for all of x. Then, show that these functions are solutions for the following equation. d²y + 9y = 0 dx2

a) Functions y1, y2,., Yn are said to be linearly independent on an interval I if the equation c1y1 + c2y2 + +CnYn = 0 has only a trivial solution, namely c = c2 = .. = Cn = 0 on I. By using the definition, determine whether or not y1 = sin 3x and y2 = cos 3x are linearly independent for all of x. Then, show that these functions are solutions for the following equation. d²y + 9y = 0 dx2

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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a) Functions y1, Y2,., Yn are said to be linearly independent on an interval I if the equation cy1 + c2y2 + +CnYn = 0 has only a trivial solution, namely c = C2z = = Cn = 0 on I. By using the definition, determine whether or not y1 = sin 3x and y2 = cos 3x are linearly independent for all of x. Then, show that these functions are solutions for the following equation. d²y + 9y = 0 dx2
Transcribed Image Text:a) Functions y1, Y2,., Yn are said to be linearly independent on an interval I if the equation cy1 + c2y2 + +CnYn = 0 has only a trivial solution, namely c = C2z = = Cn = 0 on I. By using the definition, determine whether or not y1 = sin 3x and y2 = cos 3x are linearly independent for all of x. Then, show that these functions are solutions for the following equation. d²y + 9y = 0 dx2
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