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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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Question
![The task is to find the inverse Laplace transform, denoted as \( L^{-1} \), of the function:
\[
\frac{2s}{(s+1)(s+2)}
\]
for \(\sigma > -1\) by evaluating the inverse transform integral.
**Explanation:**
- The expression inside the Laplace transform involves a rational function, wherein the numerator is \(2s\), and the denominator is the product of two linear factors \( (s+1) \) and \( (s+2) \).
- The condition \(\sigma > -1\) suggests a constraint on the region of convergence for the inverse Laplace transform.
- The direction specifies using the inverse Laplace transform method, which typically involves contour integration in the complex plane or possibly using partial fraction decomposition to simplify the expression and then applying known inverse transforms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71f6a4b8-527f-4030-b85a-828002701c6f%2F672a8954-5bfb-4df7-9d64-e335fb438b42%2Fy833yb7_processed.png&w=3840&q=75)
Transcribed Image Text:The task is to find the inverse Laplace transform, denoted as \( L^{-1} \), of the function:
\[
\frac{2s}{(s+1)(s+2)}
\]
for \(\sigma > -1\) by evaluating the inverse transform integral.
**Explanation:**
- The expression inside the Laplace transform involves a rational function, wherein the numerator is \(2s\), and the denominator is the product of two linear factors \( (s+1) \) and \( (s+2) \).
- The condition \(\sigma > -1\) suggests a constraint on the region of convergence for the inverse Laplace transform.
- The direction specifies using the inverse Laplace transform method, which typically involves contour integration in the complex plane or possibly using partial fraction decomposition to simplify the expression and then applying known inverse transforms.
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