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Beliebt Rechnen >

inverselaplace ((e^{-s}))/(s^2-6s+9)

Lösung

inverse laplace transformation

\frac{( e ^{- s} )}{s ^{2} - 6 s + 9}

Lösung

H (t - 1) e^{3 (t - 1)} (t - 1)

Schritte zur Lösung

L^{- 1} {\frac{( e ^{- s} )}{s ^{2} - 6 s + 9}}

Faktorisiere

s^{2} - 6 s + 9 : (s - 3)^{2}

= L^{- 1} {\frac{e ^{- s}}{( s - 3 ) ^{2}}}

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

L^{- 1} {\frac{1}{( s - 3 ) ^{2}}} : e^{3 t} t

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

Beliebte Beispiele

y^{^{'}} = \frac{2 y}{t} + t

integral of (1-u)/(1+u)

\int \frac{1 - u}{1 + u} d u

limit as x approaches 0 of 2sin(x)-1

x \to 0 lim (2 sin (x) - 1)

integral of ((ln(x))/(x^2))

\int (\frac{ln ( x )}{x ^{2}}) d x

d/(dz)(sqrt(1-z^2))

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