y^'=xy-x

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

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

2 x - 6 y^{2} \frac{d y}{d x} + 4 = 0

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

(3 x^{2} + 2)^{2} y^{^{'}} - x y^{2} = 0, y (0) = \frac{3}{2}

\frac{x d x}{1 + x ^{2}} = \frac{d y}{y}