What is laplacetransform 2(t+2) ?

The answer to laplacetransform 2(t+2) is 2/(s^2)+4/s

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laplacetransform 2(t+2)

laplace transform

2 (t + 2)

\frac{2}{s ^{2}} + \frac{4}{s}

Solution steps

L {2 (t + 2)}

Expand

2 (t + 2) : 2 t + 4

= L {2 t + 4}

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)}

= 2 L {t} + L {4}

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

L {4} : \frac{4}{s}

= 2 \cdot \frac{1}{s ^{2}} + \frac{4}{s}

Refine

2 \frac{1}{s ^{2}} + \frac{4}{s} : \frac{2}{s ^{2}} + \frac{4}{s}

= \frac{2}{s ^{2}} + \frac{4}{s}

\frac{d}{d x} (\frac{2 x}{x ^{6} + 3 x ^{2}})

arccos (3 x)

\int u sin (u) d u

x y + y^{^{'}} = 2 x, y (0) = 5

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 4 x^{2}

What is laplacetransform 2(t+2) ?
The answer to laplacetransform 2(t+2) is 2/(s^2)+4/s