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\begin{align} \frac{dy}{dx}=\frac{1}{x^2+y^2} \end{align}

The reference answer is $(-\infty,\infty)$,or $(-\infty,0)$ or$(0,\infty)$. I don't know how to deal with the origin.

Ychen
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  • Please elaborate your query, its not understandable what are you asking for – Deeponjit Bose Mar 25 '23 at 04:42
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    Questions about the same equation: https://math.stackexchange.com/questions/2835521/limit-of-function-as-x-to-infty-when-fx-is-given and about the inverse function of the solution https://math.stackexchange.com/questions/2348022/riccati-d-e-vertical-asymptotes – Lutz Lehmann Mar 25 '23 at 12:20

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