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}}}

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

1 - y^{2} d x = (1 + x^{2}) y d y, y (0) = 0

y^{^{'}} = \frac{( 1 - 2 x )}{y}, y (1) = - 2

y^{^{'}} = \frac{1}{y ^{2}}, y (1) = 1

x d y + y d x = 2 x^{2} y d x

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)}}