I've hit a wall on the question I'm working on. Can someone look over my work and see where I may have possible gone wrong?
The question is:
Show that if is a solution of Bessel's equation of order p, then, is a solution of .
Here is my working.
Considering that is a solution, then:
Subing into ,
I simplify to find:
As , that means .
Making the substitution of
I get the following:
That equation is soo close to Bessel's equation. I go through my working and I can't find why I have those b's are there.
Thank you very much for your time.
The next part of the question is to use what it given above, and find a general solution for
I have no idea how to do this. I can try to relate coefficients of this DE to the one I mentioned in my first thread, but that doesn't work. Substituting doesn't seem to work either...