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

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

Popular >

inverse oflaplace s/((s+4))

inverse laplace

\frac{s}{( s + 4 )}

δ (t) - 4 e^{- 4 t}

Solution steps

L^{- 1} {\frac{s}{( s + 4 )}}

Take the partial fraction of

\frac{s}{s + 4} : 1 - \frac{4}{s + 4}

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

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

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

L^{- 1} {1} : δ (t)

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

= δ (t) - 4 e^{- 4 t}

\frac{\partial}{\partial x} (x^{3} y^{5} - 2 x^{2} y + x)

\int_{0}^{2} (x^{3} - 3 x^{2} + 2 x) d x

\frac{d}{d x} (csc (\frac{ln ( x + 3 )}{x ^{2}}))

\int e^{y^{2}} y d y

\int \frac{( 3 x ^{2} - x + 2 e )}{x ^{2}} d x

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