What is the solution for (dP)/(dt)=1P(500-P) ?

The solution for (dP)/(dt)=1P(500-P) is P=(500)/(-e^{-500t-c_{1)}+1}

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(dP)/(dt)=1P(500-P)

\frac{d P}{d t} = 1 P (500 - P)

P = \frac{500}{- e ^{- 500 t - c_{1}} + 1}

Solution steps

\frac{d P}{d t} = 1 P (500 - P)

Solve Bernoulli ODE:

P = \frac{500}{- e ^{- 500 t - c_{1}} + 1}

P = \frac{500}{- e ^{- 500 t - c_{1}} + 1}

- sin (3 x)

x \cdot y^{^{'}} + y = \frac{1}{y ^{2}}

\int 2 x 1 + 4 x^{2} d x

\frac{d}{d x} (cos (7^{6 x}))

x^{2} \frac{d y}{d x} + x y = 1

What is the solution for (dP)/(dt)=1P(500-P) ?
The solution for (dP)/(dt)=1P(500-P) is P=(500)/(-e^{-500t-c_{1)}+1}