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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d y}{d t} = 10 y - 2 y^{2}

\frac{d y}{d x} = (\frac{2 x + x y ^{2}}{4 y + y x ^{2}})

\frac{d y}{d x} = x y^{2}, y (1) = 1

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

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