What is the solution for (dP)/(dt)=(P-P^2) ?

The solution for (dP)/(dt)=(P-P^2) is P=-(e^{t+c_{1}})/(1-e^{t+c_{1)}}

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(dP)/(dt)=(P-P^2)

\frac{d P}{d t} = (P - P^{2})

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

Solution steps

\frac{d P}{d t} = (P - P^{2})

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}}}

What is the solution for (dP)/(dt)=(P-P^2) ?
The solution for (dP)/(dt)=(P-P^2) is P=-(e^{t+c_{1}})/(1-e^{t+c_{1)}}