What is the solution for (dP)/(dt)=0.09P(1-P/(200)) ?

The solution for (dP)/(dt)=0.09P(1-P/(200)) is P=-(200e^{0.09t+c_{1}})/(1-e^{0.09t+c_{1)}}

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(dP)/(dt)=0.09P(1-P/(200))

\frac{d P}{d t} = 0.09 P (1 - \frac{P}{200})

P = - \frac{200 e ^{0.09 t + c_{1}}}{1 - e ^{0.09 t + c_{1}}}

Solution steps

\frac{d P}{d t} = 0.09 P (1 - \frac{P}{200})

Solve separable ODE:

P = - \frac{200 e ^{0.09 t + c_{1}}}{1 - e ^{0.09 t + c_{1}}}

P = - \frac{200 e ^{0.09 t + c_{1}}}{1 - e ^{0.09 t + c_{1}}}

\frac{d y}{d x} = \frac{12 x}{y}

\frac{d y}{d x} = - 2 y^{\frac{3}{2}} tan (x)

\frac{d y}{d t} = - 0.2 y

P^{^{'}} = 0.2 P

x^{^{'}} = k x

What is the solution for (dP)/(dt)=0.09P(1-P/(200)) ?
The solution for (dP)/(dt)=0.09P(1-P/(200)) is P=-(200e^{0.09t+c_{1}})/(1-e^{0.09t+c_{1)}}