- #1
member 428835
Homework Statement
$$y'' + \frac{1}{x}y' - \lambda y = 0$$
where ##x \to \infty \implies y \to 0## and ##x \to 0 \implies y' \to 0##
The Attempt at a Solution
to begin, this was initially a pde, and I've applied separation of variables. to solve this ODE, it seems i cannot assume ##y=e^{rx}## since the ##x^{-1}## term is present. I've thought of a series solution like ##\Sigma_{-\infty}^{\infty} A_n x^n## but the boundary conditions are bringing me to a stop.
any advice would be great! how would you solve this??