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 ?