What is the solution for (dy)/(dt)=ky(1-y) ?

The solution for (dy)/(dt)=ky(1-y) is y=-(e^{kt+c_{1}})/(1-e^{kt+c_{1)}}

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(dy)/(dt)=ky(1-y)

\frac{d y}{d t} = k y (1 - y)

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

Solution steps

\frac{d y}{d t} = k y (t) (1 - y)

Solve separable ODE:

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

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

\int x x^{2} + 5 d x

\int (- x + 3)^{2} d x

(ln (ln (x)))^{^{'}}

f (x) = x^{3} (3 - x)^{2}

y = cot^{2} (sin (x))

What is the solution for (dy)/(dt)=ky(1-y) ?
The solution for (dy)/(dt)=ky(1-y) is y=-(e^{kt+c_{1}})/(1-e^{kt+c_{1)}}