What is the solution for (dx)/(dt)=rx(1-x/2) ?

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

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(dx)/(dt)=rx(1-x/2)

\frac{d x}{d t} = r x (1 - \frac{x}{2})

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

Solution steps

\frac{d x}{d t} = r x (t) (1 - \frac{x}{2})

Solve separable ODE:

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

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

y^{^{'}} + tan (5 \cdot x) y = 0

x^{^{'}} = 0.075 x - 9000

(3 y^{2} - 8 x^{- 1} y) d x + (3 x y - 8) d y = 0

cos (8 y) d y = - sin (2 x) d x

(t^{2} + 1) y^{^{'}} - \frac{t + 2}{y} = 0

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