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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 :)

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marked as duplicate by Martin Sleziak, Quixotic, David Mitra, Srivatsan, Jonas Teuwen Dec 8 '11 at 23:43

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Yes, it's duplicate. I asked again because nobody answered there. Can you help me? –  gov Dec 8 '11 at 22:21

1 Answer 1

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 $u \to 0-$.

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Thanks, I'll try to use these hints the best I can :) I'm new here, so I don't know to use all possibilities of this yet. –  gov Dec 8 '11 at 23:46

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