According to Mathworld, if in [itex]y''+P(x)y'+Q(x)y=0[/itex], P diverges at [itex]x=x_0[/itex] quicker than [itex]\frac{1}{(x-x_0)}[/itex] or Q diverges at [itex]x=x_0[/itex] quicker than [itex]\frac{1}{(x-x_0)^2}[/itex] then [itex]x_0[/itex] is called an essential singularity.(adsbygoogle = window.adsbygoogle || []).push({});

What I don't understand is that let's suppose Q diverges like [itex]\frac{1}{(x-x_0)^5}[/itex]. In that case x_0 would be called an essential singularity. But what I don't understand is that to me it looks like a pole of order 5, not an essential singularity (pole of order infinity).

Am I missing something?

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# Singularities classification in DE's

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