What is the solution for (dP)/(dt)=P(1-P) ?

The solution for (dP)/(dt)=P(1-P) is P=-(e^{t+c_{1}})/(1-e^{t+c_{1)}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dP)/(dt)=P(1-P)

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

P = - \frac{e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

Solution steps

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

Solve separable ODE:

P = - \frac{e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

P = - \frac{e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

\frac{d}{d x} (\frac{ln ( 2 x - 1 )}{x ^{2} - 1})

x \to 0 lim (x^{2} + 5 x + 6)

x \to 1 + lim (1 - x)

\int_{0}^{1} \frac{x ^{9}}{x ^{10} - 1} d x

\frac{d}{d x} (sin (x) - cos (x))

What is the solution for (dP)/(dt)=P(1-P) ?
The solution for (dP)/(dt)=P(1-P) is P=-(e^{t+c_{1}})/(1-e^{t+c_{1)}}