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15. Find the value(s) of y such that the solution of the initial-value problem y" – 4 y = sin x; y(0) = y, y (0) = 0 is bounded on [0, ∞). 3

15. Find the value(s) of y such that the solution of the initial-value problem y" – 4 y = sin x; y(0) = y, y (0) = 0 is bounded on [0, ∞). 3

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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15 & 16

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**Problem 15:** Find the value(s) of \(\gamma\) such that the solution of the initial-value problem \[ y'' - 4y = \sin x; \quad y(0) = \gamma, \quad y'(0) = 0 \] is bounded on \([0, \infty)\). Solution: \(\gamma = 3\) --- **Problem 16:** Find the value of \(\delta\) such that the solution of the initial-value problem \[ y' - 3y = 2e^{-2x}; \quad y(0) = \delta \] has limit 0 as \(x \to \infty\).
Transcribed Image Text:**Problem 15:** Find the value(s) of \(\gamma\) such that the solution of the initial-value problem \[ y'' - 4y = \sin x; \quad y(0) = \gamma, \quad y'(0) = 0 \] is bounded on \([0, \infty)\). Solution: \(\gamma = 3\) --- **Problem 16:** Find the value of \(\delta\) such that the solution of the initial-value problem \[ y' - 3y = 2e^{-2x}; \quad y(0) = \delta \] has limit 0 as \(x \to \infty\).
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