What is laplacetransform-5t^2e^{-4t}+sin(3t) ?

The answer to laplacetransform-5t^2e^{-4t}+sin(3t) is -(10)/((s+4)^3)+3/(s^2+9)

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laplacetransform-5t^2e^{-4t}+sin(3t)

laplace transform

- 5 t^{2} e^{- 4 t} + sin (3 t)

- \frac{10}{( s + 4 ) ^{3}} + \frac{3}{s ^{2} + 9}

Solution steps

L {- 5 e^{- 4 t} t^{2} + sin (3 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)}

= - 5 L {t^{2} e^{- 4 t}} + L {sin (3 t)}

L {t^{2} e^{- 4 t}} : \frac{2}{( s + 4 ) ^{3}}

L {sin (3 t)} : \frac{3}{s ^{2} + 9}

= - 5 \cdot \frac{2}{( s + 4 ) ^{3}} + \frac{3}{s ^{2} + 9}

Refine

- 5 \frac{2}{( s + 4 ) ^{3}} + \frac{3}{s ^{2} + 9} : - \frac{10}{( s + 4 ) ^{3}} + \frac{3}{s ^{2} + 9}

= - \frac{10}{( s + 4 ) ^{3}} + \frac{3}{s ^{2} + 9}

\frac{d}{d x} (x^{3} - 7 x^{2} + 14 x - 6)

\frac{\partial}{\partial u} (\frac{u}{v + 1})

\int g e^{- 2 c t} d t

x \to - 1 lim (\frac{x + 1}{1 - x ^{2}})

x \to 5 + lim (\frac{5}{x - 5})

What is laplacetransform-5t^2e^{-4t}+sin(3t) ?
The answer to laplacetransform-5t^2e^{-4t}+sin(3t) is -(10)/((s+4)^3)+3/(s^2+9)