Q5RP In Problems 3鈥�10, determine th... [FREE SOLUTION]

91影视

Fundamentals Of Differential Equations And Boundary Value Problems

R. Kent Nagle, Edward B. Saff, Arthur David Snider

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 616 pages

ISBN: 9780321977069

Chapter 7: Q5RP (page 415)

In Problems 3鈥�10, determine the Laplace transform of the given function.
$e^{2 t} - t^{3} + t^{2} - s i n 5 t$

Short Answer

Expert verified

$L {e^{2 t} - t^{3} + t^{2} - s i n 5 t} = \frac{1}{s - 2} - \frac{6}{s^{4}} + \frac{2}{s^{3}} - \frac{5}{s^{2} + 25}$

Step by step solution

Step 1:Given Information

The given function is . $e^{2 t} - t^{3} + t^{2} - s i n 5 t$

Determining the Laplace transform:

Using the following Laplace transform definition, to find Laplace of given function.

$\begin{matrix} L {e^{a t}} (s) = \frac{1}{s - a} \\ L {t^{a}} (s) = \frac{a!}{s^{a + 1}} \\ L {s i n a t} (s) = \frac{a}{s^{2} + a^{2}} \end{matrix}$

Considering the Laplace transform's linearity, we get

$\begin{matrix} L {e^{2 t} - t^{3} + t^{2} - s i n 5 t} (s) = L {e^{2 t}} (s) - L {t^{3}} (s) + L {t^{2}} (s) - L {s i n 5 t} (s) \\ = \frac{1}{s 鈭� 2} 鈭� \frac{3!}{s^{4}} + \frac{2!}{s^{3}} 鈭� \frac{5}{s^{2} + 5^{2}} \\ = \frac{1}{s 鈭� 2} 鈭� \frac{0}{s^{4}} + \frac{z}{s^{3}} 鈭� \frac{5}{s^{2} + 25} \end{matrix}$

Determining the Result

Thus, the required Laplace transform is . $L {e^{2 t} - t^{3} + t^{2} - s i n 5 t} = \frac{1}{s - 2} - \frac{6}{s^{4}} + \frac{2}{s^{3}} - \frac{5}{s^{2} + 25}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In Problems 3鈥�10, determine the Laplace transform of the given function.
$e^{2 t} - t^{3} + t^{2} - s i n 5 t$

Short Answer

Step by step solution

Step 1:Given Information

Determining the Laplace transform:

Determining the Result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

91影视

In Problems 3鈥�10, determine the Laplace transform of the given function.e2t-t3+t2-sin5t

Short Answer

Step by step solution

Step 1:Given Information

Determining the Laplace transform:

Determining the Result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 3鈥�10, determine the Laplace transform of the given function.
$e^{2 t} - t^{3} + t^{2} - s i n 5 t$