y^'=(2(1+x))/(xy)

Lösung

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

y = 4 (ln (x) + x) + c_{1}, y = - 4 (ln (x) + x) + c_{1}

Schritte zur Lösung

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

Solve separable ODE:

y = 4 (ln (x) + x) + c_{1}, y = - 4 (ln (x) + x) + c_{1}

y = 4 (ln (x) + x) + c_{1}, y = - 4 (ln (x) + x) + c_{1}

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

\frac{d y}{d x} = \frac{3 - y}{x ^{2} - 3 x + 2}

y^{^{'}} - x^{2} y = x^{2} y^{- 4}

(x^{2} y + 3 y) y^{^{'}} = 2 x y^{2} + 2 x

y^{^{'}} = 3 y (1 + y)