Consider the differential equation 4y" – 4y' + y = 0; eX/2, xeX/2. Verify that the functions ex/2 and xeX/2 form a fundamental set of solutions of the differential equation on the interval (-o, 0). The functions satisfy the differential equation and are linearly independent since W(e*/2, xex/2) = * 0 for -co

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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Consider the differential equation
4y" – 4y' + y = 0; ex/2, xeX/2
Verify that the functions ex/2 and xeX/2 form a fundamental set of solutions of the differential equation on the interval (-0, 0).
The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2)
+ 0 for -00 < x < 0.
=
Form the general solution.
y =
Transcribed Image Text:Consider the differential equation 4y" – 4y' + y = 0; ex/2, xeX/2 Verify that the functions ex/2 and xeX/2 form a fundamental set of solutions of the differential equation on the interval (-0, 0). The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) + 0 for -00 < x < 0. = Form the general solution. y =
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