What is the solution for (dP)/(dt)=aP-bP^2 ?

The solution for (dP)/(dt)=aP-bP^2 is P=-(ae^{at+c_{1}a})/(b(1-e^{a(t+c_{1))})}

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(dP)/(dt)=aP-bP^2

\frac{d P}{d t} = a P - b P^{2}

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

Solution steps

\frac{d P}{d t} = a P - b P^{2}

Solve separable ODE:

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

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

x \to 2 lim (\frac{( x + 3 )}{x - 2})

\frac{d y}{d x} = \frac{e ^{x}}{6 + e ^{x}}

cos (x), 0.5, 0 \leq x \leq π

\int (2 x - 3) tan (7 x^{2} - 21 x + 9) d x

y = \frac{x + 6}{x ^{3} + x - 7}

What is the solution for (dP)/(dt)=aP-bP^2 ?
The solution for (dP)/(dt)=aP-bP^2 is P=-(ae^{at+c_{1}a})/(b(1-e^{a(t+c_{1))})}