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Beliebt Rechnen >

inverselaplace (x+1)/(x^2-4x)

Lösung

inverse laplace transformation

\frac{x + 1}{x ^{2} - 4 x}

Lösung

- \frac{1}{4} H (t) + \frac{5}{4} e^{4 t}

Schritte zur Lösung

L^{- 1} {\frac{x + 1}{x ^{2} - 4 x}}

Ermittle den Partialbruch von

\frac{x + 1}{x ^{2} - 4 x} : - \frac{1}{4 x} + \frac{5}{4 ( x - 4 )}

= L^{- 1} {- \frac{1}{4 x} + \frac{5}{4 ( x - 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{1}{4 x}} + L^{- 1} {\frac{5}{4 ( x - 4 )}}

L^{- 1} {\frac{1}{4 x}} : \frac{1}{4} H (t)

L^{- 1} {\frac{5}{4 ( x - 4 )}} : \frac{5}{4} e^{4 t}

= - \frac{1}{4} H (t) + \frac{5}{4} e^{4 t}

Beliebte Beispiele

integral of csc^2(x)+7

\int csc^{2} (x) + 7 d x

limit as x approaches 6 of x^2-7x+6

x \to 6 lim (x^{2} - 7 x + 6)

(\partial)/(\partial x)(5yln(x))

\frac{\partial}{\partial x} (5 y ln (x))

derivative of (x^3/(3-x^2))

\frac{d}{d x} (\frac{x ^{3}}{3 - x ^{2}})

derivative 1/(2sqrt(x+10))

d er i v a t i v e \frac{1}{2 x + 10}