What is laplacetransform 1/2 (t-2)^2 ?

The answer to laplacetransform 1/2 (t-2)^2 is (1-2s+2s^2)/(s^3)

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laplacetransform 1/2 (t-2)^2

laplace transform

\frac{1}{2} (t - 2)^{2}

\frac{1 - 2 s + 2 s ^{2}}{s ^{3}}

Solution steps

L {\frac{1}{2} (t - 2)^{2}}

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)}

= \frac{1}{2} L {(t - 2)^{2}}

L {(t - 2)^{2}} : \frac{2}{s ^{3}} - \frac{4}{s ^{2}} + \frac{4}{s}

= \frac{1}{2} (\frac{2}{s ^{3}} - \frac{4}{s ^{2}} + \frac{4}{s})

Refine

\frac{1}{2} (\frac{2}{s ^{3}} - \frac{4}{s ^{2}} + \frac{4}{s}) : \frac{1 - 2 s + 2 s ^{2}}{s ^{3}}

= \frac{1 - 2 s + 2 s ^{2}}{s ^{3}}

\frac{\partial}{\partial x} (4 y + x e^{\frac{x}{y}})

y^{^{''}} - 4 y^{^{'}} + 5 y = 3 e^{2 t} sin (t)

- \frac{4 x}{x ^{2} + 1}

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What is laplacetransform 1/2 (t-2)^2 ?
The answer to laplacetransform 1/2 (t-2)^2 is (1-2s+2s^2)/(s^3)