y^'=2xy(1+y^2)

Lösung

y^{^{'}} = 2 x y (1 + y^{2})

y = \frac{e ^{2 x^{2} + 2 c_{1}}}{1 - e ^{2 (x^{2} + c_{1})}}, y = - \frac{e ^{2 x^{2} + 2 c_{1}}}{1 - e ^{2 (x^{2} + c_{1})}}

Schritte zur Lösung

y^{'} (x) = 2 x y (1 + y^{2})

Solve separable ODE:

y = \frac{e ^{2 x^{2} + 2 c_{1}}}{1 - e ^{2 (x^{2} + c_{1})}}, y = - \frac{e ^{2 x^{2} + 2 c_{1}}}{1 - e ^{2 (x^{2} + c_{1})}}

y = \frac{e ^{2 x^{2} + 2 c_{1}}}{1 - e ^{2 (x^{2} + c_{1})}}, y = - \frac{e ^{2 x^{2} + 2 c_{1}}}{1 - e ^{2 (x^{2} + c_{1})}}

\frac{d y}{d x} = x \cdot e^{y}, y (2) = 0

\frac{d p}{d t} = 0.2 p - 380

4 y^{^{'}} - 3 y - 83 = 3 y^{^{'}}

(x^{2} + 1) \frac{d y}{d x} + x y = 5 x

y^{^{'}} + \frac{y}{3} = 4