(dy)/(dx)=y^2-2y+1

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d y}{d x} = \frac{4 x}{y - 1}

\frac{d y}{d x} = cos (x) tan (y)

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

y^{^{'}} = - (1 - y) (2 - y)

y^{^{'}} = - \frac{1}{3} y^{2}