What is the solution for y^'=ry(1-y/k) ?

The solution for y^'=ry(1-y/k) is y=-(ke^{rt+c_{1}})/(1-e^{rt+c_{1)}}

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y^'=ry(1-y/k)

y^{^{'}} = ry (1 - \frac{y}{k})

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

Solution steps

y^{'} (t) = ry (t) (1 - \frac{y}{k})

Solve separable ODE:

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

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

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x \to 0 lim (x^{14} ln (x))

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\int (t e^{t} i - 4 e^{- 2 t} j + 8 t e^{t^{2}} k) d t

What is the solution for y^'=ry(1-y/k) ?
The solution for y^'=ry(1-y/k) is y=-(ke^{rt+c_{1}})/(1-e^{rt+c_{1)}}