Differential Equations Workbook For Dummies®

10.4. Answers to Laplace Transform Problems

Here are the answers to the practice questions I provide throughout this chapter. I walk you through each answer so you can see the problems worked out step by step. Enjoy!

1 What's the Laplace transform of 1 (that is, f(t) = 1)?

{1} = ?

Solution:

1. According to the definition of a Laplace transform:

   

   or

   

2. Performing the integration gives you

   

3. Okay. Now substitute in t = 0 and t = :

   

4. So {1} equals

   

   and {1} remains finite for all terms s > 0.

2 Calculate the Laplace transform of e^at (that is, f(t) = e^at):

{e^at} = ?

Solution:

1. Here's what the Laplace ...