What is the solution for (dx)/(dt)=x-x^2 ?

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

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(dx)/(dt)=x-x^2

\frac{d x}{d t} = x - x^{2}

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

Solution steps

\frac{d x}{d t} = x - x^{2}

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}}}

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\int \frac{6 x + 4}{x ^{2} ( x ^{2} + 2 )} d x

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