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

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

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

laplace transform

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

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

Solution steps

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

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

L {e^{- 2 t} t} : \frac{1}{( s + 2 ) ^{2}}

= sin (2) \frac{1}{( s + 2 ) ^{2}}

Refine

sin (2) \frac{1}{( s + 2 ) ^{2}} : \frac{sin ( 2 )}{( s + 2 ) ^{2}}

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

\frac{\partial}{\partial x} (\frac{3 x y ^{2}}{2})

\frac{d}{d x} (x^{2} - 2 x - 8)

x y^{^{'}} + y = 9 x y^{2}, y (1) = 2

x^{3} - 6 x, - 2 x

x^{2} - 6 x, - x^{2} + 6

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