2(x^2+1)(dy)/(dx)=x(4-y^2)

Lösung

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

y = - \frac{2 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}} - \frac{2}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{2 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}} - \frac{2}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}}

y = - \frac{2 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}} - \frac{2}{1 - e ^{4 c_{1}} x ^{2} - e ^{4 c_{1}}}

(1 + x^{2}) \frac{d y}{d x} + 2 x y = - x, x > 0

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

x^{3} y^{^{'}} - (8 x^{2} - 5) y = 0

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

\frac{d y}{d x} = 2 x y + 5 y, y (0) = 3