What is laplacetransform 3e^{-5t}+6e^{-3t} ?

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

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laplacetransform 3e^{-5t}+6e^{-3t}

laplace transform

3 e^{- 5 t} + 6 e^{- 3 t}

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

Solution steps

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

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)}

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

L {e^{- 5 t}} : \frac{1}{s + 5}

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

= 3 \cdot \frac{1}{s + 5} + 6 \cdot \frac{1}{s + 3}

Refine

3 \frac{1}{s + 5} + 6 \frac{1}{s + 3} : \frac{3}{s + 5} + \frac{6}{s + 3}

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

\frac{d}{d t} (\frac{4}{t ^{2}} - \frac{5}{t} - \frac{9}{5})

f (x) = x^{10}

\int_{0}^{π} 7 sin^{2} (t co) s^{4} t d t

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

x \to - 4 lim (- 2 x + 7)

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