Hi there. I'm working with the Bessel equation, and I have this problem. It says:

a) Given the equation

Use the substitution

to find the general solution

b) Find the particular solution that verifies

c) Does any solution accomplish

? Justify.

Well, so what I did is:

Then

Now I'm not pretty sure what I should do to solve this.

Multiplying by

I get the Bessel equation of order zero.

So the solution would be:

The first thing that is not clear to me is about

, with

I've got:

which gives 0/0. I know from the books that its well defined for

, so I just accepted this fact. But now, in incise b) I have to evaluate y(0), which is not defined.