What is the solution for (dP)/(dx)=0.05P(1-P/(2000)) ?

The solution for (dP)/(dx)=0.05P(1-P/(2000)) is P=-(2000e^{0.05x+c_{1}})/(1-e^{0.05x+c_{1)}}

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(dP)/(dx)=0.05P(1-P/(2000))

\frac{d P}{d x} = 0.05 P (1 - \frac{P}{2000})

P = - \frac{2000 e ^{0.05 x + c_{1}}}{1 - e ^{0.05 x + c_{1}}}

Solution steps

\frac{d P}{d x} = 0.05 P (1 - \frac{P}{2000})

Solve separable ODE:

P = - \frac{2000 e ^{0.05 x + c_{1}}}{1 - e ^{0.05 x + c_{1}}}

P = - \frac{2000 e ^{0.05 x + c_{1}}}{1 - e ^{0.05 x + c_{1}}}

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What is the solution for (dP)/(dx)=0.05P(1-P/(2000)) ?
The solution for (dP)/(dx)=0.05P(1-P/(2000)) is P=-(2000e^{0.05x+c_{1}})/(1-e^{0.05x+c_{1)}}