What is laplacetransform-5cos(5t) ?

The answer to laplacetransform-5cos(5t) is -(5s)/(s^2+25)

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laplacetransform-5cos(5t)

laplace transform

- 5 cos (5 t)

- \frac{5 s}{s ^{2} + 25}

Solution steps

L {- 5 cos (5 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)}

= - 5 L {cos (5 t)}

L {cos (5 t)} : \frac{s}{s ^{2} + 25}

= - 5 \cdot \frac{s}{s ^{2} + 25}

Refine

- 5 \frac{s}{s ^{2} + 25} : - \frac{5 s}{s ^{2} + 25}

= - \frac{5 s}{s ^{2} + 25}

x y \frac{d y}{d x} = x^{2} - y^{2}

f (x) = x + 5, at x = 4

(2 x - y) d x + (2 y - x) d y = 0

\frac{d}{d x} ((1 - x)^{- 2})

y^{^{'}} = \frac{y}{x} + 1

What is laplacetransform-5cos(5t) ?
The answer to laplacetransform-5cos(5t) is -(5s)/(s^2+25)