**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 \([0, \infty)\). \[ \quad \quad \quad \quad \quad 3 \] **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 \( x \to \infty \).
**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 \([0, \infty)\). \[ \quad \quad \quad \quad \quad 3 \] **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 \( x \to \infty \).
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.** 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 \([0, \infty)\).
\[
\quad \quad \quad \quad \quad 3
\]
**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 \( x \to \infty \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe190adae-ee45-49d2-b07b-48740048bea4%2Fe3eff89d-b54c-41ff-8ed8-20108f09fcc4%2Fiexbnd_processed.png&w=3840&q=75)
Transcribed Image Text:**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 \([0, \infty)\).
\[
\quad \quad \quad \quad \quad 3
\]
**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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