What is the solution for (dx)/(dt)=x-x^3 ?

The solution for (dx)/(dt)=x-x^3 is x=sqrt(1/(-e^{-2t-c_{1))+1}},x=-sqrt(1/(-e^{-2t-c_{1))+1}}

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(dx)/(dt)=x-x^3

\frac{d x}{d t} = x - x^{3}

x = \frac{1}{- e ^{- 2 t - c_{1}} + 1}, x = - \frac{1}{- e ^{- 2 t - c_{1}} + 1}

Solution steps

\frac{d x}{d t} = x - x^{3}

Solve Bernoulli ODE:

x = \frac{1}{- e ^{- 2 t - c_{1}} + 1}, x = - \frac{1}{- e ^{- 2 t - c_{1}} + 1}

x = \frac{1}{- e ^{- 2 t - c_{1}} + 1}, x = - \frac{1}{- e ^{- 2 t - c_{1}} + 1}

What is the solution for (dx)/(dt)=x-x^3 ?
The solution for (dx)/(dt)=x-x^3 is x=sqrt(1/(-e^{-2t-c_{1))+1}},x=-sqrt(1/(-e^{-2t-c_{1))+1}}