What is laplacetransform 2(t-3)^2+9(t-3)+11 ?

The answer to laplacetransform 2(t-3)^2+9(t-3)+11 is 4/(s^3)-3/(s^2)+2/s

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laplacetransform 2(t-3)^2+9(t-3)+11

laplace transform

2 (t - 3)^{2} + 9 (t - 3) + 11

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

Solution steps

L {2 (t - 3)^{2} + 9 (t - 3) + 11}

Expand

2 (t - 3)^{2} + 9 (t - 3) + 11 : 2 t^{2} - 3 t + 2

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

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 {2}

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

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

L {2} : \frac{2}{s}

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

Refine

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

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

y = 3 e^{4 x} + 6 e^{2 x}

\frac{d}{d x} (e^{7 x} + e^{- 7 x})

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

f (x) = 20 x - 16 x^{2}, at x = 3

y^{^{'}} + \frac{2}{t + 1} y = 3 t

What is laplacetransform 2(t-3)^2+9(t-3)+11 ?
The answer to laplacetransform 2(t-3)^2+9(t-3)+11 is 4/(s^3)-3/(s^2)+2/s