What is laplacetransform-t^2+9t-20 ?

The answer to laplacetransform-t^2+9t-20 is -2/(s^3)+9/(s^2)-(20)/s

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laplacetransform-t^2+9t-20

laplace transform

- t^{2} + 9 t - 20

- \frac{2}{s ^{3}} + \frac{9}{s ^{2}} - \frac{20}{s}

Solution steps

L {- t^{2} + 9 t - 20}

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)}

= - L {t^{2}} + 9 L {t} - L {20}

L {t^{2}} : \frac{2}{s ^{3}}

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

L {20} : \frac{20}{s}

= - \frac{2}{s ^{3}} + 9 \cdot \frac{1}{s ^{2}} - \frac{20}{s}

Refine

- \frac{2}{s ^{3}} + 9 \frac{1}{s ^{2}} - \frac{20}{s} : - \frac{2}{s ^{3}} + \frac{9}{s ^{2}} - \frac{20}{s}

= - \frac{2}{s ^{3}} + \frac{9}{s ^{2}} - \frac{20}{s}

\int \frac{6 x ^{2}}{( 2 x - 1 ) ( 2 x + 3 )} d x

(x^{2} - 3 x y) d x + x d y = 0

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} - 5 y = 4

x \to 0 lim (\frac{x ^{2} + 2 x}{x})

x (2 x + 1)^{4}

What is laplacetransform-t^2+9t-20 ?
The answer to laplacetransform-t^2+9t-20 is -2/(s^3)+9/(s^2)-(20)/s