Definition of Laplace Transform - Differential Equations

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Question

Find the Laplace Transform for the following function.

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$ \end{Bmatrix}$

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Answer

To find the Laplace Transform for the following function

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$\end{Bmatrix}$

use the transforms for basic functions which state,

$\mathcal{L}\begin{Bmatrix} 1 \end{Bmatrix}=\frac{1}{s}$$

$\mathcal{L}\begin{Bmatrix} $e^{at}$ \end{Bmatrix}=\frac{1}{s-a}$$

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$ \end{Bmatrix}=\int_0^\infty $e^{-st}$$e^{-5t}$dt=\int_0^\infty $e^{-(s+5)t}$ dt$

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Question

Find the Laplace Transform for the following function.

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$ \end{Bmatrix}$

Tap to reveal answer

Answer

To find the Laplace Transform for the following function

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$\end{Bmatrix}$

use the transforms for basic functions which state,

$\mathcal{L}\begin{Bmatrix} 1 \end{Bmatrix}=\frac{1}{s}$$

$\mathcal{L}\begin{Bmatrix} $e^{at}$ \end{Bmatrix}=\frac{1}{s-a}$$

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$ \end{Bmatrix}=\int_0^\infty $e^{-st}$$e^{-5t}$dt=\int_0^\infty $e^{-(s+5)t}$ dt$

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Question

Find the Laplace Transform for the following function.

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$ \end{Bmatrix}$

Tap to reveal answer

Answer

To find the Laplace Transform for the following function

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$\end{Bmatrix}$

use the transforms for basic functions which state,

$\mathcal{L}\begin{Bmatrix} 1 \end{Bmatrix}=\frac{1}{s}$$

$\mathcal{L}\begin{Bmatrix} $e^{at}$ \end{Bmatrix}=\frac{1}{s-a}$$

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$ \end{Bmatrix}=\int_0^\infty $e^{-st}$$e^{-5t}$dt=\int_0^\infty $e^{-(s+5)t}$ dt$

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Question

Find the Laplace Transform for the following function.

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$ \end{Bmatrix}$

Tap to reveal answer

Answer

To find the Laplace Transform for the following function

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$\end{Bmatrix}$

use the transforms for basic functions which state,

$\mathcal{L}\begin{Bmatrix} 1 \end{Bmatrix}=\frac{1}{s}$$

$\mathcal{L}\begin{Bmatrix} $e^{at}$ \end{Bmatrix}=\frac{1}{s-a}$$

$\mathcal{L}\begin{Bmatrix} $e^{-5t}$ \end{Bmatrix}=\int_0^\infty $e^{-st}$$e^{-5t}$dt=\int_0^\infty $e^{-(s+5)t}$ dt$

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