What is laplacetransform e^{-4t}\times sin(2t) ?

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

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laplacetransform e^{-4t}\times sin(2t)

laplace transform

e^{- 4 t} \cdot sin (2 t)

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

Solution steps

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

Apply transform rule:

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

then

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

For

e^{- 4 t} sin (2 t) : f (t) = sin (2 t), a = - 4

= L {sin (2 t)} (s + 4)

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

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

\frac{10}{3} x^{3} - 5 x^{2} - 11 x + 6

\int \frac{x}{100 x ^{2} - 1} d x

\frac{d y}{d x}, x = y^{18}

g (x) = 1 - x

y^{^{''}} + y = 0, y (0) = 1, y^{^{'}} (0) = 0

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