Laplace Transform of Exponential/Examples/2 e^4 t

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Example of Use of Laplace Transform of Exponential

$\laptrans {2 e^{4 t} } = \dfrac 2 {s - 4}$

for $s > 4$.


Proof

\(\displaystyle \laptrans {2 e^{4 t} }\) \(=\) \(\displaystyle 2 \laptrans {e^{4 t} }\) Linear Combination of Laplace Transforms
\(\displaystyle \) \(=\) \(\displaystyle \dfrac 2 {s - 4}\) Laplace Transform of Exponential

$\blacksquare$

Sources