What is the solution for (dy)/(dt)=0.2y(1000-y) ?

The solution for (dy)/(dt)=0.2y(1000-y) is y=(1000)/(-5e^{-200t-c_{1)}+1}

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(dy)/(dt)=0.2y(1000-y)

\frac{d y}{d t} = 0.2 y (1000 - y)

y = \frac{1000}{- 5 e ^{- 200 t - c_{1}} + 1}

Solution steps

\frac{d y}{d t} = 0.2 y (1000 - y)

Solve Bernoulli ODE:

y = \frac{1000}{- 5 e ^{- 200 t - c_{1}} + 1}

y = \frac{1000}{- 5 e ^{- 200 t - c_{1}} + 1}

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\frac{\partial}{\partial x} (5 x)

2 sin (x), 6 cos (x), [0, π]

\int \frac{( ln ( z ) ) ^{6}}{z} d z

\int \frac{1}{( a + b ) + ( a - b ) x ^{2}} d x

What is the solution for (dy)/(dt)=0.2y(1000-y) ?
The solution for (dy)/(dt)=0.2y(1000-y) is y=(1000)/(-5e^{-200t-c_{1)}+1}