Solving Differential Equations: Getting Started with Initial Conditions

[danny271828]

I need to solve the equation

\frac{d^{2}}{dx^{2}}\Psi + \frac{2}{x}\frac{d}{dx}\Psi = \lambda\Psi

Can anyone help me get a start on this problem? I've been guessing at a few solutions with no results... I'm not asking anyone to solve the problem... just a few hints on starting... maybe regarding the form

 

[dextercioby]

So it's \frac{d^{2}\Psi (x)}{dx} +\frac{2}{x}\frac{d\Psi (x)}{dx}-\lambda \Psi (x) =0.

Note the singularity at x=0. In what space do you expect the solution to be ?