What is the solution for x^'=4x-x^3 ?

The solution for x^'=4x-x^3 is x= 2/(sqrt(-e^{-8t-c_{1))+1}},x=-2/(sqrt(-e^{-8t-c_{1))+1}}

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x^'=4x-x^3

x^{^{'}} = 4 x - x^{3}

x = \frac{2}{- e ^{- 8 t - c_{1}} + 1}, x = - \frac{2}{- e ^{- 8 t - c_{1}} + 1}

Solution steps

x^{'} (t) = 4 x - x^{3}

Solve Bernoulli ODE:

x = \frac{2}{- e ^{- 8 t - c_{1}} + 1}, x = - \frac{2}{- e ^{- 8 t - c_{1}} + 1}

x = \frac{2}{- e ^{- 8 t - c_{1}} + 1}, x = - \frac{2}{- e ^{- 8 t - c_{1}} + 1}

What is the solution for x^'=4x-x^3 ?
The solution for x^'=4x-x^3 is x= 2/(sqrt(-e^{-8t-c_{1))+1}},x=-2/(sqrt(-e^{-8t-c_{1))+1}}