What is laplacetransform 24e^{-7t}-5e^{-23t} ?

The answer to laplacetransform 24e^{-7t}-5e^{-23t} is (24)/(s+7)-5/(s+23)

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laplacetransform 24e^{-7t}-5e^{-23t}

laplace transform

24 e^{- 7 t} - 5 e^{- 23 t}

\frac{24}{s + 7} - \frac{5}{s + 23}

Solution steps

L {24 e^{- 7 t} - 5 e^{- 23 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)}

= 24 L {e^{- 7 t}} - 5 L {e^{- 23 t}}

L {e^{- 7 t}} : \frac{1}{s + 7}

L {e^{- 23 t}} : \frac{1}{s + 23}

= 24 \cdot \frac{1}{s + 7} - 5 \cdot \frac{1}{s + 23}

Refine

24 \frac{1}{s + 7} - 5 \frac{1}{s + 23} : \frac{24}{s + 7} - \frac{5}{s + 23}

= \frac{24}{s + 7} - \frac{5}{s + 23}

What is laplacetransform 24e^{-7t}-5e^{-23t} ?
The answer to laplacetransform 24e^{-7t}-5e^{-23t} is (24)/(s+7)-5/(s+23)