What is laplacetransform 2/3 t^3e^{-8t} ?

The answer to laplacetransform 2/3 t^3e^{-8t} is 4/((s+8)^4)

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laplacetransform 2/3 t^3e^{-8t}

laplace transform

\frac{2}{3} t^{3} e^{- 8 t}

\frac{4}{( s + 8 ) ^{4}}

Solution steps

L {\frac{2}{3} e^{- 8 t} t^{3}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{2}{3} L {t^{3} e^{- 8 t}}

L {t^{3} e^{- 8 t}} : \frac{6}{( s + 8 ) ^{4}}

= \frac{2}{3} \cdot \frac{6}{( s + 8 ) ^{4}}

Refine

\frac{2}{3} \frac{6}{( s + 8 ) ^{4}} : \frac{4}{( s + 8 ) ^{4}}

= \frac{4}{( s + 8 ) ^{4}}

\frac{d}{d x} (3 cos (x) - sin (x))

\frac{d y}{d x} + 2 x y - y = 0, y (0) = 4

\int \frac{x + 9}{16 - ( x - 4 ) ^{2}} d x

\int (sin (x))^{11} (cos (x))^{5} d x

y^{^{'}} = y^{3} - 6 x^{2} y^{3}, y (1) = - \frac{1}{2}

What is laplacetransform 2/3 t^3e^{-8t} ?
The answer to laplacetransform 2/3 t^3e^{-8t} is 4/((s+8)^4)