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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\int \frac{x ^{2} - 22}{x ^{3} - 2 x ^{2} + x} d x

x 8^{x}

\int 9 e^{- 9 x} sin (9 x) d x

x \to 1 lim (\frac{x ^{3}}{x ^{2} + 1})

\frac{\partial}{\partial y} (y^{2} - x^{2} - 10)

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