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Beliebt Rechnen >

(dx)/(dt)= 1/(t(1-t))

Lösung

\frac{d x}{d t} = \frac{1}{t ( 1 - t )}

Lösung

x = ln (t) - ln (t - 1) + c_{1}

Schritte zur Lösung

\frac{d x}{d t} = \frac{1}{t ( 1 - t )}

Ersetze

\frac{d x}{d t}

mit

x^{'} (t)

x^{^{'}} (t) = \frac{1}{t ( 1 - t )}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

x = \int \frac{1}{t ( 1 - t )} d t

\int \frac{1}{t ( 1 - t )} d t = ln (t) - ln (t - 1) + c_{1}

x = ln (t) - ln (t - 1) + c_{1}

Graph

Beliebte Beispiele

\frac{d}{d t} (x y)

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\frac{d}{d x} (lo g_{10} (2 x - 3))