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Fundamentals Of Differential Equations And Boundary Value Problems

Found in: Page 415

Book edition 9th

Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages 616 pages

ISBN 9780321977069

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Short Answer

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

$L {e^{3 t} s i n 4 t} (s) = \frac{4}{{(s - 3)}^{2} + 16}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:Given Information

The given function is $e^{3 t} s i n 4 t$ .

Step 2: Determining the Laplace transform:

Using the Laplace transform definition, $L {e^{a t} s i n b t} (s) = \frac{b}{{(s - a)}^{2} + b^{2}}$ we get

$\begin{matrix} L {e^{3 t} s i n 4 t} (s) = \frac{4}{{(s - 3)}^{2} + 4^{2}} \\ = \frac{4}{{(s - 3)}^{2} + 16} \end{matrix}$

Step 3: Determining the Result

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

Most popular questions for Math Textbooks

Solve the given integral equation or integro-differential equation for y(t) $y (t) + 3 \int_{0}^{t} e^{t - v} y (v) d v = s i n t$

solve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution.

$w'' + w = u (t - - 2) - - u (t - - 4); w (0) = 1, w' (0) = 0$

In Problems 1-10, determine the inverse Laplace transform of the given function.

$\frac{s - 1}{2 s^{2} + s + 6}$

In Problems 1-10, determine the inverse Laplace transform of the given function.

$\frac{3 s - 15}{2 s^{2} - 4 s + 10}$

In Problems 1-20, determine the Laplace transform of the given function using Table 7.1 on page 356 and the properties of the transform given in Table 7.2. [Hint: In Problems 12-20, use an appropriate trigonometric identity.]

${tsin}^{2} t$

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