1. ## differentiating

let it be:
$
y = x^n(\cos(lnx)+\sin(lnx))
$

where n is a natyral number
Prove that this equation is true
$
x^2 y''+(1-2n)xy'+(1+n^2)y=0
$

Should i consider n here as a constant right? Cause in some similar cases, it's not mentioned that n is natyral. That's the only question

2. Originally Posted by javax
let it be:
$
y = x^n(\cos(lnx)+\sin(lnx))
$

where n is a natyral number
Prove that this equation is true
$
x^2 y''+(1-2n)xy'+(1+n^2)y=0
$

Should i consider n here as a constant right? Cause in some similar cases, it's not mentioned that n is natyral. That's the only question
it just means that n is a poistive (or non-negative, depending on your definition of the naturals) integer. integers are constants. so if that helps...