What is inverse oflaplace 3/(s+4) ?

The answer to inverse oflaplace 3/(s+4) is 3e^{-4t}

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inverse oflaplace 3/(s+4)

inverse laplace

\frac{3}{s + 4}

3 e^{- 4 t}

Solution steps

L^{- 1} {\frac{3}{s + 4}}

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

= 3 L^{- 1} {\frac{1}{s + 4}}

Use Inverse Laplace Transform table:

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

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

= 3 e^{- 4 t}

\int (5 x^{3} - 18)^{7} 15 x^{2} d x

\int \frac{4 e ^{x}}{e ^{2 x} + 10 e ^{x} + 25} d x

\frac{d y}{d x} + x^{2} y = 2 x^{2}

y^{^{'}} = (y + 2 t)^{2}

- 2 y - y^{2} d x + (3 + 2 x - x^{2}) d y = 0

What is inverse oflaplace 3/(s+4) ?
The answer to inverse oflaplace 3/(s+4) is 3e^{-4t}