(y^2+y)dx-xdy=0,y(1)=1

Lösung

(y^{2} + y) d x - x d y = 0, y (1) = 1

y = - \frac{x}{x - c _{1}}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{x}{x - c _{1}}

y = - \frac{x}{x - c _{1}}

y^{^{'}} = - x^{5} y^{2}

\frac{d y}{d x} + \frac{y}{5} = y^{- 3}

\frac{d y}{d x} = - \frac{3 cos ( x )}{y}

(x + 2)^{2} \cdot \frac{d y}{d x} = 4 x y

x y^{^{'}} = 5 y