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

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

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

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

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

Solution steps

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

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