What is inverse oflaplace (7s+5)/((s+2)(s-1)) ?

The answer to inverse oflaplace (7s+5)/((s+2)(s-1)) is 3e^{-2t}+4e^t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse oflaplace (7s+5)/((s+2)(s-1))

inverse laplace

\frac{7 s + 5}{( s + 2 ) ( s - 1 )}

3 e^{- 2 t} + 4 e^{t}

Solution steps

L^{- 1} {\frac{7 s + 5}{( s + 2 ) ( s - 1 )}}

Take the partial fraction of

\frac{7 s + 5}{( s + 2 ) ( s - 1 )} : \frac{3}{s + 2} + \frac{4}{s - 1}

= L^{- 1} {\frac{3}{s + 2} + \frac{4}{s - 1}}

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{3}{s + 2}} + L^{- 1} {\frac{4}{s - 1}}

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

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

= 3 e^{- 2 t} + 4 e^{t}

\int_{0}^{1} (x^{3}) d x

x cos (2 x)

\int \frac{( ln ^{2} ( x ^{2} ) )}{x} d x

\int \frac{8 x ^{3}}{0.2 x ^{4} + 8000} d x

\frac{\partial}{\partial y} (x^{y} + y)

What is inverse oflaplace (7s+5)/((s+2)(s-1)) ?
The answer to inverse oflaplace (7s+5)/((s+2)(s-1)) is 3e^{-2t}+4e^t