I am currently studying a great text(adsbygoogle = window.adsbygoogle || []).push({});

Elementary Differential Equations and Boundary Valued Problems 9th edition;

and we have come to chapter 5 and are studying Ordinary Points, Singular Points, and Irregular Points. (get the point?)

Anyway, I did see these mentioned,,

this Bessel equation:

x^2 y`` + x y` + (x^2 - v^2) = 0

and the Legendre equation:

(1 - x^2) y`` -2x y` [tex]\alpha[/tex] ([tex]\alpha[/tex] + 1) = 0

and since they have their own names they do "seem" important.

This is just one chapter of my studies this semester but would anyone care to inform me of any physical relevance of these equations to the real world? I'm sure they help in some way, and I suppose I could google it, but this is the physics forums and I'm sure you guys love this stuff as much as I enjoy typing this out right now. so PF's help me please!

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# Why derive Regular Singular Points?

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