(a) Solve the initial-value problem x?y" – xy + 5y = 0, y(1) = v2, y'(1) = 3/2 %3D and show that your solution can be written in the form y(x) = 2x cos(2 In x - 1/4). (b) Determine all zeros of y(x). (c) o Sketch the corresponding solution curve on the interval [0.001, 16], and verify the zeros in the interval [3, 16].

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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(a) Solve the initial-value problem
x?y" – xy + 5y = 0,
y(1) = v2, y'(1) = 3/2
%3D
and show that your solution can be written in the
form
y(x) = 2x cos(2 In x - 1/4).
(b) Determine all zeros of y(x).
(c) o Sketch the corresponding solution curve on the
interval [0.001, 16], and verify the zeros in the
interval [3, 16].
Transcribed Image Text:(a) Solve the initial-value problem x?y" – xy + 5y = 0, y(1) = v2, y'(1) = 3/2 %3D and show that your solution can be written in the form y(x) = 2x cos(2 In x - 1/4). (b) Determine all zeros of y(x). (c) o Sketch the corresponding solution curve on the interval [0.001, 16], and verify the zeros in the interval [3, 16].
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