What is laplacetransform (t-2)e^t ?

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

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laplacetransform (t-2)e^t

laplace transform

(t - 2) e^{t}

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

Solution steps

L {e^{t} (t - 2)}

Apply transform rule:

L {f (t)} = F (s)

then

L {e^{a t} f (t)} = F (s - a)

For

(t - 2) e^{t} : f (t) = (t - 2), a = 1

= L {(t - 2)} (s - 1)

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

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

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

x \to 4 - lim (\frac{∣ 4 - x ∣}{x - 4})

x \to 1 lim (3)

y^{^{'}} - 2 x y = 6 x

4 x^{3} + 2 x

y^{^{'}} = a y - b y^{3}

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