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)}}

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(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}}}

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

\frac{d P}{d t} = 7 Pt, P (1) = 5

y^{^{'}} = y sec (x)

\frac{d y}{d x} = y + \frac{y}{x ln ( x )}

\frac{d y}{d t} + 20 y = 24, y = \frac{6}{5} - \frac{6}{5} e^{- 20 t}

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)}}