What is the solution for x^'=ax(1-x/k) ?

The solution for x^'=ax(1-x/k) is x=-(ke^{at+c_{1}})/(1-e^{at+c_{1)}}

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x^'=ax(1-x/k)

x^{^{'}} = a x (1 - \frac{x}{k})

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

Solution steps

x^{'} (t) = a x (1 - \frac{x}{k})

Solve separable ODE:

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

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

What is the solution for x^'=ax(1-x/k) ?
The solution for x^'=ax(1-x/k) is x=-(ke^{at+c_{1}})/(1-e^{at+c_{1)}}