What is inverse oflaplace 1/(4s+7) ?

The answer to inverse oflaplace 1/(4s+7) is 1/4 e^{-(7t)/4}

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inverse oflaplace 1/(4s+7)

inverse laplace

\frac{1}{4 s + 7}

\frac{1}{4} e^{- \frac{7 t}{4}}

Solution steps

L^{- 1} {\frac{1}{4 s + 7}}

= L^{- 1} {\frac{1}{4} \cdot \frac{1}{s + \frac{7}{4}}}

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)}

= \frac{1}{4} L^{- 1} {\frac{1}{s + \frac{7}{4}}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{1}{s + \frac{7}{4}}} = e^{- \frac{7 t}{4}}

= \frac{1}{4} e^{- \frac{7 t}{4}}

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What is inverse oflaplace 1/(4s+7) ?
The answer to inverse oflaplace 1/(4s+7) is 1/4 e^{-(7t)/4}