What is the solution for (dx)/(dt)=kx(1000-x) ?

The solution for (dx)/(dt)=kx(1000-x) is x=(1000)/(e^{-1000kt+c_{1)}+1}

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(dx)/(dt)=kx(1000-x)

\frac{d x}{d t} = k x (1000 - x)

x = \frac{1000}{e ^{- 1000 k t + c_{1}} + 1}

Solution steps

\frac{d x}{d t} = k x (t) (1000 - x)

Solve Bernoulli ODE:

x = \frac{1000}{e ^{- 1000 k t + c_{1}} + 1}

x = \frac{1000}{e ^{- 1000 k t + c_{1}} + 1}

y^{^{''}} + 400 y = sec (20 x), y (0) = 5, y^{^{'}} (0) = - 5

\int (x - 1) sec^{2} (x) d x

(x - 1) ln (x)

\frac{\partial}{\partial x} (\frac{1}{3 x + 2})

x \to 2 - lim (g (x))

What is the solution for (dx)/(dt)=kx(1000-x) ?
The solution for (dx)/(dt)=kx(1000-x) is x=(1000)/(e^{-1000kt+c_{1)}+1}