de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

laplacetransform e^{-2(2t-4)}(1/2 (2t-4)+2)

Lösung

laplace transformation

e^{- 2 (2 t - 4)} (\frac{1}{2} (2 t - 4) + 2)

Lösung

\frac{e ^{8}}{( s + 4 ) ^{2}}

Schritte zur Lösung

L {e^{- 2 (2 t - 4)} (\frac{1}{2} (2 t - 4) + 2)}

Schreibe

e^{- 2 (2 t - 4)} (\frac{1}{2} (2 t - 4) + 2)

um:

e^{- 4 t + 8} t

= L {e^{- 4 t + 8} t}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

e^{- 4 t + 8} t : f (t) = e^{- 4 t + 8}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{- 4 t + 8}})

L {e^{- 4 t + 8}} : \frac{e ^{8}}{s + 4}

\frac{d}{d s} (\frac{e ^{8}}{s + 4}) = - \frac{e ^{8}}{( s + 4 ) ^{2}}

= (- 1)^{1} (- \frac{e ^{8}}{( s + 4 ) ^{2}})

= \frac{e ^{8}}{( s + 4 ) ^{2}}

Beliebte Beispiele

integral of-e^ysin(y)cos(y)

\int - e^{y} sin (y) cos (y) d y

integral of (1/(z^3)-3/(z^2))

\int (\frac{1}{z ^{3}} - \frac{3}{z ^{2}}) d z

(\partial)/(\partial y)(x^2+4y^2)

\frac{\partial}{\partial y} (x^{2} + 4 y^{2})

(dy)/(dx)=y+e^x

\frac{d y}{d x} = y + e^{x}

integral of sqrt((4-x^2)/(x^2))

\int \frac{4 - x ^{2}}{x ^{2}} d x