What is the solution for (dP)/(dt)=1.05P(1-P/(7500)) ?

The solution for (dP)/(dt)=1.05P(1-P/(7500)) is P=-(7500e^{1.05t+c_{1}})/(1-e^{1.05t+c_{1)}}

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(dP)/(dt)=1.05P(1-P/(7500))

\frac{d P}{d t} = 1.05 P (1 - \frac{P}{7500})

P = - \frac{7500 e ^{1.05 t + c_{1}}}{1 - e ^{1.05 t + c_{1}}}

Solution steps

\frac{d P}{d t} = 1.05 P (1 - \frac{P}{7500})

Solve separable ODE:

P = - \frac{7500 e ^{1.05 t + c_{1}}}{1 - e ^{1.05 t + c_{1}}}

P = - \frac{7500 e ^{1.05 t + c_{1}}}{1 - e ^{1.05 t + c_{1}}}

2 y (x + 1) \frac{d y}{d x} = 2 + y^{2}, y (0) = 1

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

y^{^{'}} = x^{2} y^{- 7}

x^{3} d y + x^{2} y d x + y d x = x d y

y^{^{'}} + 4 y = 0, y (0) = 5

What is the solution for (dP)/(dt)=1.05P(1-P/(7500)) ?
The solution for (dP)/(dt)=1.05P(1-P/(7500)) is P=-(7500e^{1.05t+c_{1}})/(1-e^{1.05t+c_{1)}}