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

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

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

laplace transform

e^{- 3 t} sin (2 t)

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

Solution steps

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

Apply transform rule:

L {f (t)} = F (s)

then

L {e^{a t} f (t)} = F (s - a)

For

e^{- 3 t} sin (2 t) : f (t) = sin (2 t), a = - 3

= L {sin (2 t)} (s + 3)

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

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

\frac{d}{d x} (\frac{x ^{2}}{9})

y^{^{''}} + 4 y = 2 csc^{2} (2 t)

\frac{d}{d y} (2 y^{2} e^{x y^{2}})

y = x^{2}, y = x

\frac{\partial}{\partial y} (sin (x^{2}))

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