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

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

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

laplace transform

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

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

Solution steps

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

Apply transform rule:

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

then

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

For

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

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

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

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

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

\int_{0}^{2} 9 x + 37 d x

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

\frac{d ^{2}}{d x ^{2}} (5 x^{4} - 5 x^{2} + 7)

y = 2 e^{x}

\int_{0}^{π} (9 e^{x} + 7 sin (x)) d x

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