y^'=xy^2-x

Lösung

y^{^{'}} = x y^{2} - x

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

Schritte zur Lösung

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

Solve Bernoulli ODE:

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

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

\frac{d y}{d x} = - 6 y

(tan (x) \frac{d y}{d x}) - y = a

\frac{d p}{d t} = t^{2} p - 2 p + t^{2} - 2

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

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