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I am trying to understand the definition of regular point, regular singular point and irregular point

for example, the ode. what would be the r,rs or i points of this?

x^3y'''(x)+3x^2y''(x)+4xy(x)=0

dividing gives the standard form

y''+(3/x)y' + (4/x^2)y=0

So, obviously x can't equal zero, does that make x a regular singular point because x=0 gives rise to a singularity? If so, what does "regular" mean?

Thanks,

David

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# Regular singular points (definition)

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