What is laplacetransform 2t^2-3t+3 ?

The answer to laplacetransform 2t^2-3t+3 is 4/(s^3)-3/(s^2)+3/s

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laplacetransform 2t^2-3t+3

laplace transform

2 t^{2} - 3 t + 3

\frac{4}{s ^{3}} - \frac{3}{s ^{2}} + \frac{3}{s}

Solution steps

L {2 t^{2} - 3 t + 3}

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^{2}} - 3 L {t} + L {3}

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

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

L {3} : \frac{3}{s}

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

Refine

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

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

x \to \infty lim (5 x^{4})

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

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e - 4 x, y (0) = - 6, y^{^{'}} (0) = 1

(x^{2} + 3) \cdot \frac{d y}{d x} = x y

n = 1 \sum \infty \frac{5}{n ^{5}}

What is laplacetransform 2t^2-3t+3 ?
The answer to laplacetransform 2t^2-3t+3 is 4/(s^3)-3/(s^2)+3/s