What is laplacetransform 3e^{4t-5} ?

The answer to laplacetransform 3e^{4t-5} is 3/(e^5(s-4))

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laplacetransform 3e^{4t-5}

laplace transform

3 e^{4 t - 5}

\frac{3}{e ^{5} ( s - 4 )}

Solution steps

L {3 e^{4 t - 5}}

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)}

= 3 e^{- 5} L {e^{4 t}}

L {e^{4 t}} : \frac{1}{s - 4}

= 3 e^{- 5} \frac{1}{s - 4}

Refine

3 e^{- 5} \frac{1}{s - 4} : \frac{3}{e ^{5} ( s - 4 )}

= \frac{3}{e ^{5} ( s - 4 )}

\frac{d}{d x} (20 e^{- x})

\frac{d}{d x} (\frac{2 x + x ^{2}}{( 1 + x ) ^{2}})

y^{^{'}} + 35 y = 7

- 2 t^{2} - 8 t + 9

x \to 6 - lim (\frac{x - 6}{∣ x - 6 ∣})

What is laplacetransform 3e^{4t-5} ?
The answer to laplacetransform 3e^{4t-5} is 3/(e^5(s-4))