What is laplacetransform (t^2-1)^2 ?

The answer to laplacetransform (t^2-1)^2 is (24)/(s^5)-4/(s^3)+1/s

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

laplacetransform (t^2-1)^2

laplace transform

(t^{2} - 1)^{2}

\frac{24}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

Solution steps

L {(t^{2} - 1)^{2}}

Expand

(t^{2} - 1)^{2} : t^{4} - 2 t^{2} + 1

= L {t^{4} - 2 t^{2} + 1}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{4}} - 2 L {t^{2}} + L {1}

L {t^{4}} : \frac{24}{s ^{5}}

L {t^{2}} : \frac{2}{s ^{3}}

L {1} : \frac{1}{s}

= \frac{24}{s ^{5}} - 2 \cdot \frac{2}{s ^{3}} + \frac{1}{s}

Refine

\frac{24}{s ^{5}} - 2 \frac{2}{s ^{3}} + \frac{1}{s} : \frac{24}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

= \frac{24}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

\frac{d}{d x} (x^{e^{x^{2}}})

x \to - 19 + lim (x + 19)

y = arccos (2 x)

\int e^{in x} d x

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

What is laplacetransform (t^2-1)^2 ?
The answer to laplacetransform (t^2-1)^2 is (24)/(s^5)-4/(s^3)+1/s