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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{4 d y}{( x ^{2} + 1 d x )} = \frac{1}{2 y}

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

y^{^{'}} y = t

\frac{d v}{d t} = (1 - v)

y \cdot y^{^{'}} \cdot cot (x) = y^{2} + 2