What is laplacetransform-4cos(6t) ?

The answer to laplacetransform-4cos(6t) is -(4s)/(s^2+36)

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laplacetransform-4cos(6t)

laplace transform

- 4 cos (6 t)

- \frac{4 s}{s ^{2} + 36}

Solution steps

L {- 4 cos (6 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 {cos (6 t)}

L {cos (6 t)} : \frac{s}{s ^{2} + 36}

= - 4 \cdot \frac{s}{s ^{2} + 36}

Refine

- 4 \frac{s}{s ^{2} + 36} : - \frac{4 s}{s ^{2} + 36}

= - \frac{4 s}{s ^{2} + 36}

\int (5^{x}) d x

\frac{d}{d x} (5 sin (y) + 3 e^{2 x})

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

t^{3} - 27 t

\int \frac{x ^{2} + 16 x - 16}{x ^{3} - 16 x} d x

What is laplacetransform-4cos(6t) ?
The answer to laplacetransform-4cos(6t) is -(4s)/(s^2+36)