What is the solution for (dP)/(dt)=P(a-bP) ?

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

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(dP)/(dt)=P(a-bP)

\frac{d P}{d t} = P (a - b P)

P = \frac{a}{- e ^{- a (t + c_{1})} + b}

Solution steps

\frac{d P}{d t} = P (a - b P)

Solve Bernoulli ODE:

P = \frac{a}{- e ^{- a (t + c_{1})} + b}

P = \frac{a}{- e ^{- a (t + c_{1})} + b}

y = 2 x, y = 2 x^{2} - 4

\frac{d}{d x} (∣ 2 x + 1 ∣)

\int_{1}^{8} \frac{2}{x ^{3}} d x

x \to 0 + lim ((- ln (x))^{x})

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