(dy)/(dx)-1/x y= 1/x y^3

Lösung

\frac{d y}{d x} - \frac{1}{x} y = \frac{1}{x} y^{3}

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

Schritte zur Lösung

\frac{d y}{d x} - \frac{1}{x} y = \frac{1}{x} y^{3}

Solve separable ODE:

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

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

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

y^{^{'}} = 2 y, y (0) = 6

\frac{d x}{d y} = \frac{x y}{1 + y}

y^{^{'}} - \frac{t ^{5}}{y} = 0

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