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.