What is the solution for P^'=0.05P(1-P/(400)) ?

The solution for P^'=0.05P(1-P/(400)) is P(t)=-(400e^{0.05t+c_{1}})/(1-e^{0.05t+c_{1)}}

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P^'=0.05P(1-P/(400))

P^{^{'}} = 0.05 P (1 - \frac{P}{400})

P (t) = - \frac{400 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

Solution steps

P^{'} (t) = 0.05 P (t) (1 - \frac{P ( t )}{400})

Solve separable ODE:

P (t) = - \frac{400 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

P (t) = - \frac{400 e ^{0.05 t + c_{1}}}{1 - e ^{0.05 t + c_{1}}}

What is the solution for P^'=0.05P(1-P/(400)) ?
The solution for P^'=0.05P(1-P/(400)) is P(t)=-(400e^{0.05t+c_{1}})/(1-e^{0.05t+c_{1)}}