What is the solution for (dx)/(dt)=x-x^2,x(0)=2 ?

The solution for (dx)/(dt)=x-x^2,x(0)=2 is x=-(2e^t)/(1-2e^t)

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(dx)/(dt)=x-x^2,x(0)=2

\frac{d x}{d t} = x - x^{2}, x (0) = 2

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

Solution steps

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

Solve separable ODE:

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

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

What is the solution for (dx)/(dt)=x-x^2,x(0)=2 ?
The solution for (dx)/(dt)=x-x^2,x(0)=2 is x=-(2e^t)/(1-2e^t)