What is inverse oflaplace 3/((s-7)^4) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

inverse oflaplace 3/((s-7)^4)

inverselaplace

\frac{e ^{7 t} t ^{3}}{2}

Solution steps

L^{- 1} {\frac{3}{( s - 7 ) ^{4}}}

Apply inverse transform rule:

L^{- 1} {F (s)} = f (t)

then

L^{- 1} {F (s - a)} = e^{a t} f (t)

For

\frac{3}{( s - 7 ) ^{4}} : a = 7, F (s) = \frac{3}{s ^{4}}

= e^{7 t} L^{- 1} {\frac{3}{s ^{4}}}

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

= \frac{e ^{7 t} t ^{3}}{2}

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