(y-yx^2)y‘=-(x-xy^2)
<=> y *(1-x^2) *dy/dx = -x *(1-y^2)
<=> y *(1-x^2) *dy = -x *(1-y^2) dx
<=> y/(1-y^2)dy = -x/ (1-x^2) dx
Integrieren
- ln ( y^2 - 1) / 2 = ln ( x^2 - 1 ) / 2 + C
ln ( y^2 - 1) = - ln ( x^2 - 1 ) - 2C
y^2 - 1 = 1 / (x^2 - 1 ) / e^(2C)
y = √ ( 1 + 1 / (x^2 - 1 ) / e^(2C) )