What is laplacetransform 10e^{-t/2} ?

The answer to laplacetransform 10e^{-t/2} is (20)/(2s+1)

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laplacetransform 10e^{-t/2}

laplacetransform

\frac{20}{2 s + 1}

Solution steps

L {10 e^{- \frac{t}{2}}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

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

= 10 L {e^{- \frac{1}{2} t}}

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

= 10 \cdot \frac{2}{2 s + 1}

Refine

10 \frac{2}{2 s + 1} : \frac{20}{2 s + 1}

= \frac{20}{2 s + 1}

What is laplacetransform 10e^{-t/2} ?
The answer to laplacetransform 10e^{-t/2} is (20)/(2s+1)