de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

inverselaplace ((s+1))/((s^2+s-1))

Lösung

inverse laplace transformation

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

Lösung

e^{- \frac{t}{2}} cosh (\frac{5 t}{2}) + \frac{e ^{- \frac{t}{2}} sinh ( \frac{5 t}{2} )}{5}

Schritte zur Lösung

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

Schreibe

\frac{s + 1}{s ^{2} + s - 1}

um:

\frac{s + \frac{1}{2}}{( s + \frac{1}{2} ) ^{2} - \frac{5}{4}} + \frac{1}{2} \cdot \frac{1}{( s + \frac{1}{2} ) ^{2} - \frac{5}{4}}

= L^{- 1} {\frac{s + \frac{1}{2}}{( s + \frac{1}{2} ) ^{2} - \frac{5}{4}} + \frac{1}{2} \cdot \frac{1}{( s + \frac{1}{2} ) ^{2} - \frac{5}{4}}}

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

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{s + \frac{1}{2}}{( s + \frac{1}{2} ) ^{2} - \frac{5}{4}}} + \frac{1}{2} L^{- 1} {\frac{1}{( s + \frac{1}{2} ) ^{2} - \frac{5}{4}}}

L^{- 1} {\frac{s + \frac{1}{2}}{( s + \frac{1}{2} ) ^{2} - \frac{5}{4}}} : e^{- \frac{t}{2}} cosh (\frac{5 t}{2})

L^{- 1} {\frac{1}{( s + \frac{1}{2} ) ^{2} - \frac{5}{4}}} : e^{- \frac{t}{2}} \frac{2}{5} sinh (\frac{5 t}{2})

= e^{- \frac{t}{2}} cosh (\frac{5 t}{2}) + \frac{1}{2} e^{- \frac{t}{2}} \frac{2}{5} sinh (\frac{5 t}{2})

Fasse

e^{- \frac{t}{2}} cosh (\frac{5 t}{2}) + \frac{1}{2} e^{- \frac{t}{2}} \frac{2}{5} sinh (\frac{5 t}{2})

zusammen:

e^{- \frac{t}{2}} cosh (\frac{5 t}{2}) + \frac{e ^{- \frac{t}{2}} sinh ( \frac{5 t}{2} )}{5}

= e^{- \frac{t}{2}} cosh (\frac{5 t}{2}) + \frac{e ^{- \frac{t}{2}} sinh ( \frac{5 t}{2} )}{5}

Beliebte Beispiele

((dy)/(dx))+1/y = y/2+x/y

(\frac{d y}{d x}) + \frac{1}{y} = \frac{y}{2} + \frac{x}{y}

derivative f(x)=cy^{-5}

d er i v a t i v e f (x) = c y^{- 5}

(\partial)/(\partial x)(ln(kt-mx))

\frac{\partial}{\partial x} (ln (k t - m x))

(\partial)/(\partial x)(x/(y^2)-y/(x^2))

\frac{\partial}{\partial x} (\frac{x}{y ^{2}} - \frac{y}{x ^{2}})

derivative (x^2)^{-1}

d er i v a t i v e (x^{2})^{- 1}