What is the solution for (dP)/(dt)=0.0017P(1-P/(6200)) ?

The solution for (dP)/(dt)=0.0017P(1-P/(6200)) is P=-(6200e^{0.0017t+c_{1}})/(1-e^{0.0017t+c_{1)}}

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(dP)/(dt)=0.0017P(1-P/(6200))

\frac{d P}{d t} = 0.0017 P (1 - \frac{P}{6200})

P = - \frac{6200 e ^{0.0017 t + c_{1}}}{1 - e ^{0.0017 t + c_{1}}}

Solution steps

\frac{d P}{d t} = 0.0017 P (1 - \frac{P}{6200})

Solve separable ODE:

P = - \frac{6200 e ^{0.0017 t + c_{1}}}{1 - e ^{0.0017 t + c_{1}}}

P = - \frac{6200 e ^{0.0017 t + c_{1}}}{1 - e ^{0.0017 t + c_{1}}}

\frac{d y}{d x} + 15 x^{2} y = 2 x^{2}, y (0) = 3

\frac{d x}{d t} = 80 - \frac{x}{1000}, x = 5000, t = 0

\frac{d y}{d x} = \frac{y}{1 - x ^{2}}

y^{^{'}} = 16 y - 20

\frac{d y}{d x} = 8 - 15 y

What is the solution for (dP)/(dt)=0.0017P(1-P/(6200)) ?
The solution for (dP)/(dt)=0.0017P(1-P/(6200)) is P=-(6200e^{0.0017t+c_{1}})/(1-e^{0.0017t+c_{1)}}