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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

(3 x^{2} + 2)^{3} y^{^{'}} - x y^{2} = 0

y^{^{'}} = \frac{5 ( 1 + x )}{x y}

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

\frac{d y}{d x} = 12 x^{3} y, y (0) = 2

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