Differential equation - asymptotes
$y'=y^2-yx^2+x^2-1$, $y(x_0)=y_0$. Find $x_0$ and $y_0$ such that solution has vertical asymptote $-\infty$. Help me, please :)
Hints: 1) it may help to look at the phase plane.
2) Compare this equation to $y' = y^2$.
Alternatively, look at the differential equation that you get using the change of variable $y(x) = 1/u(x)$, noting that $y \to - \infty$ corresponds to $u \to 0-$.