Q7.3-1E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

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.]

${\mathbf{t}}^{\mathbf{2}}\mathbf{+}{\mathbf{e}}^{\mathbf{t}}\mathbf{sin}\mathbf{2}\mathbf{t}$

Step-by-Step Solution

Answer

$\mathcal{L}\left\{t^2+e^t\sin 2t\right\}=\frac{2}{s^3}+\frac{2}{{(s-1)}^2+4}$

Step 1: Examine the Problem

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.]t2+etsin2t

Step 2: Apply Definitions

We use the relevant mathematical definitions to classify or identify the required elements.

Step 3: Answer

L t 2 + e t sin 2 t = 2 s 3 + 2 ( s - 1 ) 2 + 4