What is inverse oflaplace-2/((s+2)^2) ?

The answer to inverse oflaplace-2/((s+2)^2) is -e^{-2t}*2t

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inverse oflaplace-2/((s+2)^2)

inverse laplace

- \frac{2}{( s + 2 ) ^{2}}

- e^{- 2 t} \cdot 2 t

Solution steps

L^{- 1} {- \frac{2}{( s + 2 ) ^{2}}}

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)}

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

L^{- 1} {\frac{2}{( s + 2 ) ^{2}}} : e^{- 2 t} \cdot 2 t

= - e^{- 2 t} \cdot 2 t

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What is inverse oflaplace-2/((s+2)^2) ?
The answer to inverse oflaplace-2/((s+2)^2) is -e^{-2t}*2t