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

Lösung

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

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

Schritte zur Lösung

y^{'} (t) = - (1 - y) (2 - y)

Solve separable ODE:

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

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

y^{^{'}} = - \frac{1}{3} y^{2}

\frac{d y}{d x} = 60 y x^{9}

y^{^{'}} - 3 e^{5 x - 2 y} = 0

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

y^{^{'}} = 2 y - 1, y (0) = 1