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Found in: Page 415

### Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

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# In Problems 3–10, determine the Laplace transform of the given function.${{\mathbit{e}}}^{\mathbf{3}\mathbf{t}}{\mathbit{s}}{\mathbit{i}}{\mathbit{n}}{\mathbf{4}}{\mathbit{t}}$

$L\left\{{e}^{3t}sin4t\right\}\left(s\right)=\frac{4}{{\left(s-3\right)}^{2}+16}$

See the step by step solution

## Step 1:Given Information

The given function is ${e}^{3t}sin4t$.

## Step 2: Determining the Laplace transform:

Using the Laplace transform definition, $L\left\{{e}^{at}sinbt\right\}\left(s\right)=\frac{b}{{\left(s-a\right)}^{2}+{b}^{2}}$we get

$\begin{array}{c}L\left\{{e}^{3t}sin4t\right\}\left(s\right)=\frac{4}{{\left(s-3\right)}^{2}+{4}^{2}}\\ =\frac{4}{{\left(s-3\right)}^{2}+16}\end{array}$

## Step 3: Determining the Result

Thus, the required Laplace transform is .$L\left\{{e}^{3t}sin4t\right\}\left(s\right)=\frac{4}{{\left(s-3\right)}^{2}+16}$

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