What is inverse oflaplace ((12s+5))/(s(s+3)) ?

The answer to inverse oflaplace ((12s+5))/(s(s+3)) is 5/3 \H(t)+31/3 e^{-3t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse oflaplace ((12s+5))/(s(s+3))

inverse laplace

\frac{( 12 s + 5 )}{s ( s + 3 )}

\frac{5}{3} H (t) + \frac{31}{3} e^{- 3 t}

Solution steps

L^{- 1} {\frac{( 12 s + 5 )}{s ( s + 3 )}}

Take the partial fraction of

\frac{12 s + 5}{s ( s + 3 )} : \frac{5}{3 s} + \frac{31}{3 ( s + 3 )}

= L^{- 1} {\frac{5}{3 s} + \frac{31}{3 ( 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{5}{3 s}} + L^{- 1} {\frac{31}{3 ( s + 3 )}}

L^{- 1} {\frac{5}{3 s}} : \frac{5}{3} H (t)

L^{- 1} {\frac{31}{3 ( s + 3 )}} : \frac{31}{3} e^{- 3 t}

= \frac{5}{3} H (t) + \frac{31}{3} e^{- 3 t}

\frac{1}{x ^{2}} - \frac{7}{x ^{4}}

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

\frac{d}{d x} (5 ln (2 + x))

x \to 1 lim (\frac{x ^{3} - 1}{x + 1})

\int (6 x^{2}) d x

What is inverse oflaplace ((12s+5))/(s(s+3)) ?
The answer to inverse oflaplace ((12s+5))/(s(s+3)) is 5/3 \H(t)+31/3 e^{-3t}