What is inverse oflaplace (2s+5)/(s^2+5s+6) ?

The answer to inverse oflaplace (2s+5)/(s^2+5s+6) is e^{-2t}+e^{-3t}

Popular >

inverse oflaplace (2s+5)/(s^2+5s+6)

inverse laplace

\frac{2 s + 5}{s ^{2} + 5 s + 6}

e^{- 2 t} + e^{- 3 t}

Solution steps

L^{- 1} {\frac{2 s + 5}{s ^{2} + 5 s + 6}}

Take the partial fraction of

\frac{2 s + 5}{s ^{2} + 5 s + 6} : \frac{1}{s + 2} + \frac{1}{s + 3}

= L^{- 1} {\frac{1}{s + 2} + \frac{1}{s + 3}}

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} {\frac{1}{s + 2}} + L^{- 1} {\frac{1}{s + 3}}

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

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

= e^{- 2 t} + e^{- 3 t}

\frac{d}{d x} (arctan (g (x)) x)

x, x = 1

y = 3 x^{3} + x^{2} - 8 x + 4, (- 2, 0)

\int \frac{3 x}{7 - x ^{2}} d x

\frac{d}{d x} (- \frac{4 x}{( x ^{2} + 4 ) ^{2}})

What is inverse oflaplace (2s+5)/(s^2+5s+6) ?
The answer to inverse oflaplace (2s+5)/(s^2+5s+6) is e^{-2t}+e^{-3t}