What is laplacetransform 5e-3(t-2) ?

The answer to laplacetransform 5e-3(t-2) is (5e)/s-3/(s^2)+6/s

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laplacetransform 5e-3(t-2)

laplace transform

5 e - 3 (t - 2)

\frac{5 e}{s} - \frac{3}{s ^{2}} + \frac{6}{s}

Solution steps

L {5 e - 3 (t - 2)}

Expand

5 e - 3 (t - 2) : 5 e - 3 t + 6

= L {5 e - 3 t + 6}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {5 e} - 3 L {t} + L {6}

L {5 e} : \frac{5 e}{s}

L {t} : \frac{1}{s ^{2}}

L {6} : \frac{6}{s}

= \frac{5 e}{s} - 3 \cdot \frac{1}{s ^{2}} + \frac{6}{s}

Refine

\frac{5 e}{s} - 3 \frac{1}{s ^{2}} + \frac{6}{s} : \frac{5 e}{s} - \frac{3}{s ^{2}} + \frac{6}{s}

= \frac{5 e}{s} - \frac{3}{s ^{2}} + \frac{6}{s}

\frac{\partial}{\partial x} (3 x^{2} y + 2 x y^{2})

x \to 3 lim (tan (\frac{3 π}{4}))

\int \frac{1}{2 x + x} d x

\int r e^{\frac{r}{3}} d r

\frac{\partial}{\partial x} (x^{2} + y^{2} - y^{2} x - 2)

What is laplacetransform 5e-3(t-2) ?
The answer to laplacetransform 5e-3(t-2) is (5e)/s-3/(s^2)+6/s