(dp)/(p-p^2)=dt

Lösung

\frac{d p}{p - p ^{2}} = d t

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

Schritte zur Lösung

\frac{d p}{p - p ^{2}} = d t

Lass

t

die abhängige Variable sein. Teile durch

d p

\frac{1}{p - p ^{2}} = \frac{d t}{d p}

Ersetze

\frac{d t}{d p}

mit

t^{'} (p)

\frac{1}{p - p ^{2}} = t^{^{'}} (p)

Isoliere

t^{'} (p) : t^{'} (p) = \frac{1}{p - p ^{2}}

Wenn

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

dann

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

t = \int \frac{1}{p - p ^{2}} d p

\int \frac{1}{p - p ^{2}} d p = ln (p) - ln (p - 1) + c_{1}

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

\frac{d}{d x} (3 x^{4} + 2 x^{3} + x^{2} - 2)

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

\frac{d y}{d x} = - \frac{y ( x + y + 1 )}{x + 2 y}

\int \frac{1}{e ^{x} + 3} d x

d er i v a t i v e y = sin (x) ln (2 x)