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Can someone please explain the green text to me?

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Maybe I am not reading it right, but that sentence makes no sense to me. "that (2) is an equation For which $xp(x)$ and $x^2q(x)$ " what does this part mean? The next part that follows sys something about being constants. Are they trying to say we should replace equation (2) with $xp(x)$ and $x^2q(x)$ like

$y''(x) + xp(x)y'(x) + x^2q(x)y(x) = 0 $ So that

$y''(x) + p_0y'(x) + q_0y(x) = 0$

Either case it makes no sense to me at all, especially why they started writing out the $xp(x)$ as a series.

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    It makes perfect sense to me!2012-06-23

1 Answers 1

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Right below Eq. (2) it is said that $p(x)=p_0/x, \ q(x)=q_0/x^2$ which means $xp(x)$ and $x^2q(x)$ are constants. Later on he assumes that these functions are not constants!

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    @jak Because (2) is an equation for $y$ (which is unknown), not for $p_0$ and $q_0$ (which are considered to be given). The sentence in green would be clearer if it said "equation **in** which..."2012-06-23