Take this example: $y'=y^2+1$. There's no "real equilibrium", but is it right to say it has two "complex equilibria"? If so, what should be the conclusion of the derivative test? $$y'' = 2y \implies 2i>0 \vee 2i<0?$$
2026-05-06 01:20:38.1778030438
How to analyze ODE equilibrium stability with complex equilibria
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