What is inverse oflaplace (15)/(3s+sqrt(3)) ?

The answer to inverse oflaplace (15)/(3s+sqrt(3)) is 5e^{-t/(sqrt(3))}

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inverse oflaplace (15)/(3s+sqrt(3))

inverse laplace

\frac{15}{3 s + 3}

5 e^{- \frac{t}{3}}

Solution steps

L^{- 1} {\frac{15}{3 s + 3}}

= L^{- 1} {5 \cdot \frac{1}{s + \frac{1}{3}}}

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 + \frac{1}{3}}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{1}{s + \frac{1}{3}}} = e^{- \frac{t}{3}}

= 5 e^{- \frac{t}{3}}

\int \frac{x ^{3} + 2 x}{x ^{4} + 4 x ^{2} + 3} d x

\frac{d y}{d t} + 0.7 t y = 7 t, y (0) = 7

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (2 x)

\frac{d}{d x} (\frac{50}{x ^{9}})

\int \frac{8}{4 - x ^{2}} d x

What is inverse oflaplace (15)/(3s+sqrt(3)) ?
The answer to inverse oflaplace (15)/(3s+sqrt(3)) is 5e^{-t/(sqrt(3))}