Undergrad Help - Derivation of Pulsating Star Euler ODE

[Kajan thana]

TL;DR

Hi guys, this is not a homework question, I am trying to rewrite the Pulsating Star model equation to another form.

to

I am a bit clueless on how to get break the $r X(r)$ from inside the derivative.P.S. I tried to copy from Symbolab instead of pasting the picture, but it didn't let me.

 

[jedishrfu]

Summary:: Hi guys, this is not a homework question, I am trying to rewrite the Pulsating Star model equation to another form.

$\frac{1}{r}\frac{d^2}{dr^2}\left[rX\left(r\right)\right]-\frac{l\left(l+1\right)}{r^2}X\left(r\right)=0$

to

$rX^{''}+2rX^{'}-l\left(l+1\right)X=0$

I am a bit clueless on how to get break the $r X(r)$ from inside the derivative.

I added double # to each of your expressions both front and back to get them to render correctly with MathJax. Please take some time to read our Latex reference guide via the link in my signature below.

ADDENDUM: I forgot to mention the single quote in the second term of the last equation needed to be written as 2rX^{'} and not 2rX^'

 

[Kajan thana]

I added double # to each of your expressions both front and back to get them to render correctly with MathJax. Please take some time to read our Latex reference guide via the link in my signature below.

Thank you for that

 

[mfb]

Just apply the product rule for derivatives (you'll need it twice) and at the end multiply the whole expression by r².