What is laplacetransform 2t*sin(t) ?

The answer to laplacetransform 2t*sin(t) is (4s)/((s^2+1)^2)

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laplacetransform 2t*sin(t)

laplace transform

2 t \cdot sin (t)

\frac{4 s}{( s ^{2} + 1 ) ^{2}}

Solution steps

L {2 t sin (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 sin (t)}

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

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

Refine

2 \frac{2 s}{( s ^{2} + 1 ) ^{2}} : \frac{4 s}{( s ^{2} + 1 ) ^{2}}

= \frac{4 s}{( s ^{2} + 1 ) ^{2}}

t y^{^{'}} - y = \frac{- t ^{3}}{y ^{2}}

7 x (\frac{d y}{d x}) = 2 x e^{x} - 7 y + 6 x^{2}

x \to 2 lim ((4 x - 3) (x^{2} + 5))

arcsin (\frac{2}{x ^{2}})

\int_{4}^{9} 2 x x d x

What is laplacetransform 2t*sin(t) ?
The answer to laplacetransform 2t*sin(t) is (4s)/((s^2+1)^2)