What is the solution for (dP)/(dt)=0.08P(1-P/(1000)) ?

The solution for (dP)/(dt)=0.08P(1-P/(1000)) is P=-(1000e^{0.08t+c_{1}})/(1-e^{0.08t+c_{1)}}

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(dP)/(dt)=0.08P(1-P/(1000))

\frac{d P}{d t} = 0.08 P (1 - \frac{P}{1000})

P = - \frac{1000 e ^{0.08 t + c_{1}}}{1 - e ^{0.08 t + c_{1}}}

Solution steps

\frac{d P}{d t} = 0.08 P (1 - \frac{P}{1000})

Solve separable ODE:

P = - \frac{1000 e ^{0.08 t + c_{1}}}{1 - e ^{0.08 t + c_{1}}}

P = - \frac{1000 e ^{0.08 t + c_{1}}}{1 - e ^{0.08 t + c_{1}}}

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What is the solution for (dP)/(dt)=0.08P(1-P/(1000)) ?
The solution for (dP)/(dt)=0.08P(1-P/(1000)) is P=-(1000e^{0.08t+c_{1}})/(1-e^{0.08t+c_{1)}}