What is laplacetransform (5e^{9t}-4)e^{-6t} ?

The answer to laplacetransform (5e^{9t}-4)e^{-6t} is 5/(s-3)-4/(s+6)

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laplacetransform (5e^{9t}-4)e^{-6t}

laplace transform

(5 e^{9 t} - 4) e^{- 6 t}

\frac{5}{s - 3} - \frac{4}{s + 6}

Solution steps

L {e^{- 6 t} (5 e^{9 t} - 4)}

Apply transform rule:

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

then

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

For

(5 e^{9 t} - 4) e^{- 6 t} : f (t) = (5 e^{9 t} - 4), a = - 6

= L {(5 e^{9 t} - 4)} (s + 6)

L {(5 e^{9 t} - 4)} : \frac{5}{s - 9} - \frac{4}{s}

= \frac{5}{( s + 6 ) - 9} - \frac{4}{( s + 6 )}

= \frac{5}{s - 3} - \frac{4}{s + 6}

(t)^{2}

\int \frac{4}{81 - ( x + 9 ) ^{2}} d x

y^{^{'}} + 7 y = 3

\int \frac{x - 4}{x ( x - 1 ) ^{2}} d x

x \to 2 lim (\frac{x - 2}{x - 2})

What is laplacetransform (5e^{9t}-4)e^{-6t} ?
The answer to laplacetransform (5e^{9t}-4)e^{-6t} is 5/(s-3)-4/(s+6)