What is laplacetransform 2tcos(t) ?

The answer to laplacetransform 2tcos(t) is -(2(-s^2+1))/((s^2+1)^2)

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laplacetransform 2tcos(t)

laplace transform

2 t cos (t)

- \frac{2 ( - s ^{2} + 1 )}{( s ^{2} + 1 ) ^{2}}

Solution steps

L {2 t cos (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)}

= 2 L {t cos (t)}

L {t cos (t)} : - \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}}

= 2 (- \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}})

Refine

2 (- \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}}) : - \frac{2 ( - s ^{2} + 1 )}{( s ^{2} + 1 ) ^{2}}

= - \frac{2 ( - s ^{2} + 1 )}{( s ^{2} + 1 ) ^{2}}

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

x \to - 8 + lim (\frac{x + 9}{x + 8})

f (x) = x^{2} - 2 x, at x = - 2

\int \frac{1}{t ^{5}} d t

f (x) = x^{4} + 6 x^{2} - x, (1, 6)

What is laplacetransform 2tcos(t) ?
The answer to laplacetransform 2tcos(t) is -(2(-s^2+1))/((s^2+1)^2)