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Beliebt Rechnen >

(5du)/(dt)=u^2

Lösung

\frac{5 d u}{d t} = u^{2}

Lösung

t = - \frac{5}{u} + c_{1}

Schritte zur Lösung

\frac{5 d u}{d t} = u^{2}

Lass

t

die abhängige Variable sein. Teile durch

d u

:

\frac{5}{\frac{d t}{d u}} = u^{2}

Ersetze

\frac{d t}{d u}

mit

t^{'} (u)

\frac{5}{t ^{^{'}} ( u )} = u^{2}

Isoliere

t^{'} (u) : t^{'} (u) = \frac{5}{u ^{2}}

Wenn

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

dann

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

t = \int \frac{5}{u ^{2}} d u

\int \frac{5}{u ^{2}} d u = - \frac{5}{u} + c_{1}

t = - \frac{5}{u} + c_{1}

Graph

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