L{t-3^(-3t)} which of the laplace transform is 1) L{t-3^(-3t)}=1/s^2+1/(s-3) 2) L{t-3^(-3t)}=1/s^2-1/(s-3)

Question

$L {t - e^{- 3 t}}$
which of the laplace transform is
$1.) L {t - e^{- 3 t}} = \frac{1}{s^{2}} + \frac{1}{s - 3}$
$2.) L {t - e^{- 3 t}} = \frac{1}{s^{2}} - \frac{1}{s - 3}$
$3.) L {t - e^{- 3 t}} = \frac{1}{s^{2}} + \frac{1}{s + 3}$
$4.) L {t - e^{- 3 t}} = \frac{1}{s^{2}} - \frac{1}{s + 3}$

Answer 1

Step 1
We know the Laplace transforms

L {t^{n}} = \frac{n!}{s^{n + 1}}, s > 0

L {e^{a t}} = \frac{1}{(s - a)}, s > 0

Now, L {t - e^{- 3 t}} = L {t} - L {e^{- 3 t}}

L {t} = \frac{1}{s^{2}}, s > 0

L {t - e^{- 3 t}} = - \frac{1}{s + 3}, s > - 3

L {t - e^{- 3 t}} = \frac{1}{s^{2}} - \frac{1}{(s + 3)}

Step 2
Answer:

L {t - e^{- 3 t}} = \frac{1}{s^{2}} - \frac{1}{s + 3}

option 4) is correct

L{t-3^(-3t)} which of the laplace transform is 1) L{t-3^(-3t)}=1/s^2+1/(s-3) 2) L{t-3^(-3t)}=1/s^2-1/(s-3)

Want to know more about Laplace transform?

Expert Answer

Not exactly what you’re looking for?

Relevant Questions