What is laplacetransform 4e^{-7t}*cos(9t) ?

The answer to laplacetransform 4e^{-7t}*cos(9t) is (4(s+7))/((s+7)^2+81)

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laplacetransform 4e^{-7t}*cos(9t)

laplace transform

4 e^{- 7 t} \cdot cos (9 t)

\frac{4 ( s + 7 )}{( s + 7 ) ^{2} + 81}

Solution steps

L {4 e^{- 7 t} cos (9 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)}

= 4 L {e^{- 7 t} cos (9 t)}

L {e^{- 7 t} cos (9 t)} : \frac{s + 7}{( s + 7 ) ^{2} + 81}

= 4 \cdot \frac{s + 7}{( s + 7 ) ^{2} + 81}

Refine

4 \frac{s + 7}{( s + 7 ) ^{2} + 81} : \frac{4 ( s + 7 )}{( s + 7 ) ^{2} + 81}

= \frac{4 ( s + 7 )}{( s + 7 ) ^{2} + 81}

f (x) = sin (x) - \frac{1}{3} sin (3 x) + \frac{1}{5} sin (5 x)

\int 1 - e^{- x^{2}} d x

sin (y)

\int \frac{1}{x ( x + 4 )} d x

\int x \cdot 9^{2 x^{2} - 8} d x

What is laplacetransform 4e^{-7t}*cos(9t) ?
The answer to laplacetransform 4e^{-7t}*cos(9t) is (4(s+7))/((s+7)^2+81)