What is laplacetransform e^{3a-2bt} ?

The answer to laplacetransform e^{3a-2bt} is (e^{3a})/(s+2b)

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laplacetransform e^{3a-2bt}

laplace transform

e^{3 a - 2 b t}

\frac{e ^{3 a}}{s + 2 b}

Solution steps

L {e^{3 a - 2 b t}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= e^{3 a} L {e^{- 2 b t}}

L {e^{- 2 b t}} : \frac{1}{s + 2 b}

= e^{3 a} \frac{1}{s + 2 b}

Refine

e^{3 a} \frac{1}{s + 2 b} : \frac{e ^{3 a}}{s + 2 b}

= \frac{e ^{3 a}}{s + 2 b}

\int \frac{4}{x ^{2} + 4 x + 8} d x

n = 1 \sum \infty \frac{3}{2 n + 3}

\int (5 e^{- 0.4 x}) d x

e^{- 2 x}

x \to 3 lim (\frac{3 - 27}{x - 3})

What is laplacetransform e^{3a-2bt} ?
The answer to laplacetransform e^{3a-2bt} is (e^{3a})/(s+2b)