What is the solution for (dp)/(dt)=3p-p^2 ?

The solution for (dp)/(dt)=3p-p^2 is p=-(3e^{3t+3c_{1}})/(1-e^{3(t+c_{1))}}

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(dp)/(dt)=3p-p^2

\frac{d p}{d t} = 3 p - p^{2}

p = - \frac{3 e ^{3 t + 3 c_{1}}}{1 - e ^{3 (t + c_{1})}}

Solution steps

\frac{d p}{d t} = 3 p - p^{2}

Solve separable ODE:

p = - \frac{3 e ^{3 t + 3 c_{1}}}{1 - e ^{3 (t + c_{1})}}

p = - \frac{3 e ^{3 t + 3 c_{1}}}{1 - e ^{3 (t + c_{1})}}

\frac{d y}{d x} = \frac{ln ( x ^{6} )}{x y ^{2}}, y (1) = 5

y - 2 y^{^{'}} = 5

y^{^{'}} = \frac{7 x ^{2} - 1}{7 + 8 y}

\frac{d y}{d x} = \frac{sin ( y )}{x}

\frac{d y}{d x} = \frac{4 y ln ( y )}{x}

What is the solution for (dp)/(dt)=3p-p^2 ?
The solution for (dp)/(dt)=3p-p^2 is p=-(3e^{3t+3c_{1}})/(1-e^{3(t+c_{1))}}