(dy)/(dt)=2y(1-y/5)

Lösung

\frac{d y}{d t} = 2 y (1 - \frac{y}{5})

y = - \frac{5 e ^{2 t + c_{1}}}{1 - e ^{2 t + c_{1}}}

Schritte zur Lösung

\frac{d y}{d t} = 2 y (1 - \frac{y}{5})

Solve separable ODE:

y = - \frac{5 e ^{2 t + c_{1}}}{1 - e ^{2 t + c_{1}}}

y = - \frac{5 e ^{2 t + c_{1}}}{1 - e ^{2 t + c_{1}}}

y^{^{'}} - 3 t y = 5 t

x y^{^{'}} - 9 y^{2} = 0

x \cdot y^{^{'}} - 2 y \cdot ln (x) = 0

\frac{d y}{d x} = sin (x) e^{2 y}

\frac{d y}{d x} = x^{2} (y + 3)