What is laplacetransform 2(sin(2t))e^{-2t} ?

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

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laplacetransform 2(sin(2t))e^{-2t}

laplace transform

2 (sin (2 t)) e^{- 2 t}

\frac{4}{( s + 2 ) ^{2} + 4}

Solution steps

L {2 e^{- 2 t} (sin (2 t))}

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)}

= 2 L {sin (2 t) e^{- 2 t}}

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

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

Refine

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

= \frac{4}{( s + 2 ) ^{2} + 4}

\frac{d}{d x} (x ln (\frac{x}{4}))

\frac{2}{s ^{2}}

x \to 5 lim (10)

\int sin^{7} (x co) s^{4} x d x

\frac{\partial}{\partial x} (6 y^{9} x^{5} - 5 y^{8} x^{4})

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