What is the solution for (dx)/(dt)=x(1-1/2500 x) ?

The solution for (dx)/(dt)=x(1-1/2500 x) is x=-(2500e^{t+c_{1}})/(1-e^{t+c_{1)}}

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(dx)/(dt)=x(1-1/2500 x)

\frac{d x}{d t} = x (1 - \frac{1}{2500} x)

x = - \frac{2500 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

Solution steps

\frac{d x}{d t} = x (1 - \frac{1}{2500} x)

Solve separable ODE:

x = - \frac{2500 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

x = - \frac{2500 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

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What is the solution for (dx)/(dt)=x(1-1/2500 x) ?
The solution for (dx)/(dt)=x(1-1/2500 x) is x=-(2500e^{t+c_{1}})/(1-e^{t+c_{1)}}