(dx)/(dt)=r(1-x/k)x

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

x y^{^{'}} = y + 1

(1 - x^{2}) y d y - x e^{- y} d x = 0

\frac{d y}{d x} - 24 x^{3} y = 0

y^{^{'}} = (y - 1) (y - 2)

y^{^{'}} = y (1 + x^{2})