Say we have an ODE(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{d^{2}x}{d^{2}y}+ p(x)\frac{dx}{dy}+q(x)y=0[/itex]

Now, we introduce a point of interest [itex]x_{0}[/itex]

If p(x) and q(x) remain finite at at [itex]x_{0}[/itex]

is [itex]x_{0}[/itex]

considered as an

ordinary point ?

Now let's do some multiplication with [itex]x_{0}[/itex]

still being

the point of interest

[itex](x-x_{0})p(x)[/itex] (1)

and

[itex](x-x_{0})^{2}q(x)[/itex] (2)

If (1) and (2) remain finite, is [itex]x_{0}[/itex]

considered as a regular singular point ?

Otherwise if (1) and (2) are undefined, is [itex]x_{0}[/itex]

an irregular singular point ?

thanks in advance

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# Ordinary points, regular singular points and irregular singular points

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