What is the solution for (dP)/(dt)=0.2P-0.001P^2 ?

The solution for (dP)/(dt)=0.2P-0.001P^2 is P=(200}{-1000e^{\frac{-c_{1}-t)/5}+1}

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(dP)/(dt)=0.2P-0.001P^2

\frac{d P}{d t} = 0.2 P - 0.001 P^{2}

P = \frac{200}{- 1000 e ^{\frac{- c _{1} - t}{5}} + 1}

Solution steps

\frac{d P}{d t} = 0.2 P - 0.001 P^{2}

Solve Bernoulli ODE:

P = \frac{200}{- 1000 e ^{\frac{- c _{1} - t}{5}} + 1}

P = \frac{200}{- 1000 e ^{\frac{- c _{1} - t}{5}} + 1}

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What is the solution for (dP)/(dt)=0.2P-0.001P^2 ?
The solution for (dP)/(dt)=0.2P-0.001P^2 is P=(200}{-1000e^{\frac{-c_{1}-t)/5}+1}