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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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