What is the solution for (dx)/(dt)=ax-bx^2-0 ?

The solution for (dx)/(dt)=ax-bx^2-0 is x= a/(-e^{-a(t+c_{1))}+b}

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(dx)/(dt)=ax-bx^2-0

\frac{d x}{d t} = a x - b x^{2} - 0

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

Solution steps

\frac{d x}{d t} = a x (t) - b x (t)^{2} - 0

Solve Bernoulli ODE:

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

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

\frac{2 x ^{2} + 4 x + 2}{x}

y = 4 x^{3} - 4 x

\int_{- 1}^{1} \frac{1}{x ^{\frac{1}{3}}} d x

\int_{0}^{\infty} e^{- b t} d t

\int \frac{x ^{2}}{4} - 1 d x

What is the solution for (dx)/(dt)=ax-bx^2-0 ?
The solution for (dx)/(dt)=ax-bx^2-0 is x= a/(-e^{-a(t+c_{1))}+b}