2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. By determining constants C1, C2, C3, C4, which are not all
zero and are such that
C1fi + C2f2 + C3 ƒ3 + C4 ƒ4 = 0 identically, show that the
functions
fi = x, f2 = e*, f3 = xe*, f4 = (2 – 3x) e*
-
are linearly dependent.
2. Show that e*, sin x, cos x are linearly independent using
Wronskian Method.
Transcribed Image Text:Description 1. By determining constants C1, C2, C3, C4, which are not all zero and are such that C1fi + C2f2 + C3 ƒ3 + C4 ƒ4 = 0 identically, show that the functions fi = x, f2 = e*, f3 = xe*, f4 = (2 – 3x) e* - are linearly dependent. 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.
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