Question

find this general solution

Answer 1

\[x^2y"+xy"+(9x^2-4)y=0\] on \[0, \infty\]

Answer 2

wat can i guess for y?

y = \[\sum_{n=0}^{\infty}c_nx^r\] ?

Answer 3

Your equation is in the form of an 'Euler Equation'
\[x^2y''+\alpha xy'+by=f(x)\]

Answer 4

no because i have \[9x^2-4\] where Q(x) and i think u cant not have that for euler eqaution

Answer 5

hmm, your right.

Answer 6

i must use power series to solve but idk what is my guess to make for y.

Answer 7

there is 1 test i think but idk how to use it.
i dont know how to know if you have singular regular point or ordinary point. so i can know which formulae to use

Answer 8

@Mertsj

Answer 9

thank you 4 u help tho :)

Answer 10

@joemath314159