What is laplacetransform e^{-t}e^{3t} ?

The answer to laplacetransform e^{-t}e^{3t} is 1/(s-2)

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laplacetransform e^{-t}e^{3t}

laplace transform

e^{- t} e^{3 t}

\frac{1}{s - 2}

Solution steps

L {e^{- t} e^{3 t}}

Apply transform rule:

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

then

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

For

e^{- t} e^{3 t} : f (t) = e^{3 t}, a = - 1

= L {e^{3 t}} (s + 1)

L {e^{3 t}} : \frac{1}{s - 3}

= \frac{1}{( s + 1 ) - 3}

= \frac{1}{s - 2}

y = x^{2} + 3.5 x + 4 π, at x = - 4

x \to 0 + lim (\frac{x ^{2} e ^{\frac{1}{x}}}{1 + x ^{2}})

y^{^{'}} = \frac{x + 3}{y + 8}

f (x) = x^{2} - 9 x + 118

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

What is laplacetransform e^{-t}e^{3t} ?
The answer to laplacetransform e^{-t}e^{3t} is 1/(s-2)