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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

y \cdot \frac{d y}{d x} + 2 x - 1 = 0

2 \frac{d y}{d x} = - 4 y + 5

\frac{d y}{d x} = x y, x (1) = 4

(x + 1) (t^{2} + 1) = t \frac{d x}{d t}

y^{^{'}} = - 4 x y + 8 x