What is laplacetransform 6t^2+3t+7 ?

The answer to laplacetransform 6t^2+3t+7 is (12)/(s^3)+3/(s^2)+7/s

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laplacetransform 6t^2+3t+7

laplace transform

6 t^{2} + 3 t + 7

\frac{12}{s ^{3}} + \frac{3}{s ^{2}} + \frac{7}{s}

Solution steps

L {6 t^{2} + 3 t + 7}

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)}

= 6 L {t^{2}} + 3 L {t} + L {7}

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

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

L {7} : \frac{7}{s}

= 6 \cdot \frac{2}{s ^{3}} + 3 \cdot \frac{1}{s ^{2}} + \frac{7}{s}

Refine

6 \frac{2}{s ^{3}} + 3 \frac{1}{s ^{2}} + \frac{7}{s} : \frac{12}{s ^{3}} + \frac{3}{s ^{2}} + \frac{7}{s}

= \frac{12}{s ^{3}} + \frac{3}{s ^{2}} + \frac{7}{s}

y^{^{'}} + 4 y = 12

3 (x + 1), 4 (x + 1), x = 3

\frac{d}{d x} (4 x + sec^{2} (2 x))

\frac{7 x ^{2} + 5 x + 3}{x}

y^{^{''}} + 9 y = cos (10 t)

What is laplacetransform 6t^2+3t+7 ?
The answer to laplacetransform 6t^2+3t+7 is (12)/(s^3)+3/(s^2)+7/s