(x^2y+3y)y^'=2xy^2+2x

Lösung

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

y = e^{2 c_{1}} x^{4} + 6 e^{2 c_{1}} x^{2} + 9 e^{2 c_{1}} - 1, y = - e^{2 c_{1}} x^{4} + 6 e^{2 c_{1}} x^{2} + 9 e^{2 c_{1}} - 1

Schritte zur Lösung

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

Solve separable ODE:

y = e^{2 c_{1}} x^{4} + 6 e^{2 c_{1}} x^{2} + 9 e^{2 c_{1}} - 1, y = - e^{2 c_{1}} x^{4} + 6 e^{2 c_{1}} x^{2} + 9 e^{2 c_{1}} - 1

y = e^{2 c_{1}} x^{4} + 6 e^{2 c_{1}} x^{2} + 9 e^{2 c_{1}} - 1, y = - e^{2 c_{1}} x^{4} + 6 e^{2 c_{1}} x^{2} + 9 e^{2 c_{1}} - 1

y^{^{'}} = 3 y (1 + y)

y^{^{'}} x - y - 1 = 0

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

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

(sec (x)) d y = 2 y + 1 d x