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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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\frac{d}{d x} (\frac{4 x ^{3} + 9}{x})

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