(dy)/(dx)xy+x=2

Lösung

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

y = 4 ln (x) - 2 x + c_{1}, y = - 4 ln (x) - 2 x + c_{1}

Schritte zur Lösung

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

Solve separable ODE:

y = 4 ln (x) - 2 x + c_{1}, y = - 4 ln (x) - 2 x + c_{1}

y = 4 ln (x) - 2 x + c_{1}, y = - 4 ln (x) - 2 x + c_{1}

x^{^{'}} = x

y^{^{'}} - 3 x^{2} y = x^{2}

y^{2} d x + 2 x^{2} d y = 0

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

\frac{d y}{d x} = x y^{2}, y (2) = - \frac{2}{5}