Find the inverse Laplace transform of the given function. 7! F(s) = (s – 6)* c-'{F(s)} =
Find the inverse Laplace transform of the given function. 7! F(s) = (s – 6)* c-'{F(s)} =
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 given function.
\[ F(s) = \frac{7!}{(s - 6)^8} \]
\[ \mathcal{L}^{-1} \{ F(s) \} = \text{(Your Answer Here)} \]
**Explanation:**
We are asked to compute the inverse Laplace transform of the function \( F(s) = \frac{7!}{(s - 6)^8} \).
To solve this, use the formula for the inverse Laplace transform of
\[ \frac{n!}{(s-a)^{n+1}} \]
which corresponds to
\[ t^n e^{at} \]
In this case, set \( n = 7 \) and \( a = 6 \).
Therefore, the inverse Laplace transform is:
\[ \mathcal{L}^{-1} \{ F(s) \} = t^7 e^{6t} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F83eb3156-1b4a-423a-812e-57012c069de9%2F3a5b6a18-662b-48be-9d3b-3e0deeb19a3a%2Fdui55hv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the inverse Laplace transform of the given function.
\[ F(s) = \frac{7!}{(s - 6)^8} \]
\[ \mathcal{L}^{-1} \{ F(s) \} = \text{(Your Answer Here)} \]
**Explanation:**
We are asked to compute the inverse Laplace transform of the function \( F(s) = \frac{7!}{(s - 6)^8} \).
To solve this, use the formula for the inverse Laplace transform of
\[ \frac{n!}{(s-a)^{n+1}} \]
which corresponds to
\[ t^n e^{at} \]
In this case, set \( n = 7 \) and \( a = 6 \).
Therefore, the inverse Laplace transform is:
\[ \mathcal{L}^{-1} \{ F(s) \} = t^7 e^{6t} \]
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