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Beliebt Rechnen >

inverselaplace (e^{-s})/(((s-3)(s+1)))

Lösung

inverse laplace transformation

\frac{e ^{- s}}{( ( s - 3 ) ( s + 1 ) )}

Lösung

H (t - 1) (\frac{1}{4} e^{3 (t - 1)} - \frac{1}{4} e^{- t + 1})

Schritte zur Lösung

L^{- 1} {\frac{e ^{- s}}{( ( s - 3 ) ( s + 1 ) )}}

Wende inverse Transformationsregel an: if

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

dann

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

Wo

H (t)

Heaviside (Schritt) Funktion ist

= H (t - 1) L^{- 1} {\frac{1}{( s - 3 ) ( s + 1 )}} (t - 1)

L^{- 1} {\frac{1}{( s - 3 ) ( s + 1 )}} : \frac{1}{4} e^{3 t} - \frac{1}{4} e^{- t}

= H (t - 1) (\frac{1}{4} e^{3 (t - 1)} - \frac{1}{4} e^{- (t - 1)})

= H (t - 1) (\frac{1}{4} e^{3 (t - 1)} - \frac{1}{4} e^{- t + 1})

Beliebte Beispiele

derivative of 4x^{(-1/8})

\frac{d}{d x} (4 x^{\frac{- 1}{8}})

(\partial)/(\partial x)(5x^{0.75}y^{0.25})

\frac{\partial}{\partial x} (5 x^{0.75} y^{0.25})

integral of ((ln(x))^{24})/x

\int \frac{( ln ( x ) ) ^{24}}{x} d x

f(x)=ln(x^{ln(x)})

f (x) = ln (x^{l n (x)})

integral from-infinity to-1 of e^{-20t}

\int_{- \infty}^{- 1} e^{- 20 t} d t