What is the solution for (dN)/(dt)=rN(t)(1-N/2) ?

The solution for (dN)/(dt)=rN(t)(1-N/2) is N=-(2e^{rt+c_{1}})/(1-e^{rt+c_{1)}}

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(dN)/(dt)=rN(t)(1-N/2)

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d x}{d y} = \frac{- 1}{x ^{2} y ^{2}}

\frac{d y}{d x} y = \frac{2}{3} x^{\frac{2}{3}} + 6 x^{3}

y e^{y} d y = \frac{1 + e ^{- 2 x}}{e ^{x}} d x

y^{^{'}} sec (x) = 7 y^{2}, y (\frac{9 π}{2}) = \frac{1}{4}

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

What is the solution for (dN)/(dt)=rN(t)(1-N/2) ?
The solution for (dN)/(dt)=rN(t)(1-N/2) is N=-(2e^{rt+c_{1}})/(1-e^{rt+c_{1)}}