y^'=2y(1-y/5)

Lösung

y^{^{'}} = 2 y (1 - \frac{y}{5})

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

Schritte zur Lösung

y^{'} (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}}}

x d y = 3 y d x

y^{^{'}} = 2 y, y (0) = 3

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

y^{^{'}} = \frac{x}{e ^{y}}

\frac{d y}{d x} = e^{x - 2 y} + \frac{1}{e ^{2 y}}