What is laplacetransform 6t^3+5cos(2t) ?

The answer to laplacetransform 6t^3+5cos(2t) is (36)/(s^4)+(5s)/(s^2+4)

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laplacetransform 6t^3+5cos(2t)

laplace transform

6 t^{3} + 5 cos (2 t)

\frac{36}{s ^{4}} + \frac{5 s}{s ^{2} + 4}

Solution steps

L {6 t^{3} + 5 cos (2 t)}

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^{3}} + 5 L {cos (2 t)}

L {t^{3}} : \frac{6}{s ^{4}}

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

= 6 \cdot \frac{6}{s ^{4}} + 5 \cdot \frac{s}{s ^{2} + 4}

Refine

6 \frac{6}{s ^{4}} + 5 \frac{s}{s ^{2} + 4} : \frac{36}{s ^{4}} + \frac{5 s}{s ^{2} + 4}

= \frac{36}{s ^{4}} + \frac{5 s}{s ^{2} + 4}

\frac{d}{d x} (x^{2} 8 x - 5)

n = 0 \sum \infty 4 (\frac{1}{10})^{n}

t^{2} y^{^{'}} + t y = 7

\int \frac{x ^{2}}{( x ^{2} + 4 ) ^{\frac{3}{2}}} d x

f (x) = \frac{27}{5 e ^{2}} - \frac{3}{2}

What is laplacetransform 6t^3+5cos(2t) ?
The answer to laplacetransform 6t^3+5cos(2t) is (36)/(s^4)+(5s)/(s^2+4)