What is the solution for (dP)/(dt)=0.02P(1-P/(250000)) ?

The solution for (dP)/(dt)=0.02P(1-P/(250000)) is P=-(250000e^{0.02t+c_{1}})/(1-e^{0.02t+c_{1)}}

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(dP)/(dt)=0.02P(1-P/(250000))

\frac{d P}{d t} = 0.02 P (1 - \frac{P}{250000})

P = - \frac{250000 e ^{0.02 t + c_{1}}}{1 - e ^{0.02 t + c_{1}}}

Solution steps

\frac{d P}{d t} = 0.02 P (1 - \frac{P}{250000})

Solve separable ODE:

P = - \frac{250000 e ^{0.02 t + c_{1}}}{1 - e ^{0.02 t + c_{1}}}

P = - \frac{250000 e ^{0.02 t + c_{1}}}{1 - e ^{0.02 t + c_{1}}}

What is the solution for (dP)/(dt)=0.02P(1-P/(250000)) ?
The solution for (dP)/(dt)=0.02P(1-P/(250000)) is P=-(250000e^{0.02t+c_{1}})/(1-e^{0.02t+c_{1)}}