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

Example of Use of Laplace Transform of Exponential

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

for $s > 4$.

Proof

\(\ds \laptrans {2 e^{4 t} }\)

\(=\)

\(\ds 2 \laptrans {e^{4 t} }\)

Linear Combination of Laplace Transforms

\(\ds \)

\(=\)

\(\ds \dfrac 2 {s - 4}\)

Laplace Transform of Exponential

$\blacksquare$

Sources

• 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Supplementary Problems: Laplace Transforms of Elementary Functions: $51 \ \text {(a)}$