What is the solution for (dx)/(dt)=x(1-x) ?

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

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(dx)/(dt)=x(1-x)

\frac{d x}{d t} = x (1 - x)

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

Solution steps

\frac{d x}{d t} = x (1 - x)

Solve separable ODE:

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

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

\int 6 ln (x^{2} - 1) d x

\frac{d}{d t} (ln (t))

\frac{\partial}{\partial x} (e^{- j w n})

y^{^{''}} + 2 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{\partial}{\partial x} (2 e^{x^{3} y})

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