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}}}

y^{^{'}} = - 0.00003 (y - 288.03) (y - 961.97)

\frac{d y}{d x} = 4 x (y^{2} + 1)

\frac{d y}{d t} = 4 - y

y^{^{'}} = x + x y

\frac{1 + cos ( 2 x )}{1 + sin ( y )} + \frac{d y}{d x} = 0

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)}}