(a) Determine if the following sets of functions are linearly dependent or linearly independent on R. (i) е ", —2е2х + 5e -x (ii) x|x|, x² (b) Consider of the solutions is W (y1, Y2) = eª. Find p(x) and q(x) and write the DE. Y1 and Y2 as two solutions for the following DE where y1 = x-1 and the Wronskian y" + p(x) y' + q(x) y = 0
(a) Determine if the following sets of functions are linearly dependent or linearly independent on R. (i) е ", —2е2х + 5e -x (ii) x|x|, x² (b) Consider of the solutions is W (y1, Y2) = eª. Find p(x) and q(x) and write the DE. Y1 and Y2 as two solutions for the following DE where y1 = x-1 and the Wronskian y" + p(x) y' + q(x) y = 0
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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Transcribed Image Text:(a) Determine if the following sets of functions are linearly dependent or linearly independent on
IR.
-x¸ -2e2a + 5e¬ª
-x
(ii) x|x|, x?
(b) Consider
of the solutions is W (y1, Y2) = e². Find p(x) and q(x) and write the DE.
Y1
and
Y2 as two solutions for the following DE where y1 = x-1 and the Wronskian
y" + p(x) y' + q(x) y = 0
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