Find the inverse Laplace transform of 68 +4 8²-4 8>2
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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![**Problem Statement:**
Find the inverse Laplace transform of the function:
\[
\frac{6s + 4}{s^2 - 4}
\]
subject to the condition \( s > 2 \).
**Details:**
- The numerator of the function is \( 6s + 4 \).
- The denominator is \( s^2 - 4 \), which can be factored as \( (s - 2)(s + 2) \).
- The region of convergence is specified as \( s > 2 \).
To solve this problem, we will use partial fraction decomposition to express the given function in a form suitable for applying known inverse Laplace transforms. Once decomposed, we will identify standard Laplace transform pairs and perform the inverse operation to find the time-domain function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29c74d06-0f3b-4eb2-9c9d-dbbc1918002c%2F8cbad734-709c-4340-ac3c-13c344ed5fac%2Fdihku1_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the inverse Laplace transform of the function:
\[
\frac{6s + 4}{s^2 - 4}
\]
subject to the condition \( s > 2 \).
**Details:**
- The numerator of the function is \( 6s + 4 \).
- The denominator is \( s^2 - 4 \), which can be factored as \( (s - 2)(s + 2) \).
- The region of convergence is specified as \( s > 2 \).
To solve this problem, we will use partial fraction decomposition to express the given function in a form suitable for applying known inverse Laplace transforms. Once decomposed, we will identify standard Laplace transform pairs and perform the inverse operation to find the time-domain function.
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