What is laplacetransform 6(t-4) ?

The answer to laplacetransform 6(t-4) is 6/(s^2)-(24)/s

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laplacetransform 6(t-4)

laplace transform

6 (t - 4)

\frac{6}{s ^{2}} - \frac{24}{s}

Solution steps

L {6 (t - 4)}

Expand

6 (t - 4) : 6 t - 24

= L {6 t - 24}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= 6 L {t} - L {24}

L {t} : \frac{1}{s ^{2}}

L {24} : \frac{24}{s}

= 6 \cdot \frac{1}{s ^{2}} - \frac{24}{s}

Refine

6 \frac{1}{s ^{2}} - \frac{24}{s} : \frac{6}{s ^{2}} - \frac{24}{s}

= \frac{6}{s ^{2}} - \frac{24}{s}

\frac{\partial}{\partial x} (e^{\frac{1}{x}})

\int \frac{x + 1}{x ^{2} + x + 1} d x

\frac{d y}{d t} + 3 y = 11, y (0) = 1

\int \frac{- 4 x}{2 x + 1} d x

y^{^{''}} - 2 y^{^{'}} + 2 y = 6

What is laplacetransform 6(t-4) ?
The answer to laplacetransform 6(t-4) is 6/(s^2)-(24)/s