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

The answer to laplacetransform 3e^{-2t}cos(3t) is (3(s+2))/((s+2)^2+9)

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

laplace transform

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

\frac{3 ( s + 2 )}{( s + 2 ) ^{2} + 9}

Solution steps

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

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

L {e^{- 2 t} cos (3 t)} : \frac{s + 2}{( s + 2 ) ^{2} + 9}

= 3 \cdot \frac{s + 2}{( s + 2 ) ^{2} + 9}

Refine

3 \frac{s + 2}{( s + 2 ) ^{2} + 9} : \frac{3 ( s + 2 )}{( s + 2 ) ^{2} + 9}

= \frac{3 ( s + 2 )}{( s + 2 ) ^{2} + 9}

x \to 3 lim (\frac{1}{3 - x})

y^{^{'}} = \frac{4 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

\int x^{3} x^{2} - 81 d x

\int \frac{cot ^{3} ( x )}{5} d x

\frac{d}{d y} ((\frac{y}{8})^{4} + \frac{1}{4 y ^{2}})

What is laplacetransform 3e^{-2t}cos(3t) ?
The answer to laplacetransform 3e^{-2t}cos(3t) is (3(s+2))/((s+2)^2+9)