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}}

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} - 6 x = 4 e^{- 2 t}

\int - 36 cos (x) d x

\int 1 + y d y

x \to 0 lim (\frac{3 x ^{2}}{x})

y = (x^{3} - 3 x) (2 x^{2} + 3 x + 5)

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)