What is inverse oflaplace 5/(s+5) ?

The answer to inverse oflaplace 5/(s+5) is 5e^{-5t}

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inverse oflaplace 5/(s+5)

inverse laplace

\frac{5}{s + 5}

5 e^{- 5 t}

Solution steps

L^{- 1} {\frac{5}{s + 5}}

= L^{- 1} {5 \cdot \frac{1}{s + 5}}

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= 5 L^{- 1} {\frac{1}{s + 5}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

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

= 5 e^{- 5 t}

What is inverse oflaplace 5/(s+5) ?
The answer to inverse oflaplace 5/(s+5) is 5e^{-5t}