y^'=(y^2)/x-1/x

Lösung

y^{^{'}} = \frac{y ^{2}}{x} - \frac{1}{x}

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d y}{d x} = - \frac{x}{y}, y (1) = 2

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

\frac{d x}{d t} = 3 x + 4

\frac{d}{d x} (x^{2} + y^{2}) = 0

(8 + x) y^{^{'}} = (x + 9) (y - 8)