How to convert Sturm Liouville to into Bessel's eqn.

[fantastic_dan]

Hello, I've been given a Sturm Liouville problem to solve:

xy" + 2y' + λxy = 0

y(∏) = 2, y(2∏) = 0

I'm not sure how to solve this problem. However, it looks similar to Bessel's equation. Any ideas?

Thanks,
Daniel

 

[LCKurtz]

Hello, I've been given a Sturm Liouville problem to solve:

xy" + 2y' + λxy = 0

y(∏) = 2, y(2∏) = 0

I'm not sure how to solve this problem. However, it looks similar to Bessel's equation. Any ideas?

Thanks,
Daniel

I would suggest trying a series solution noting $x=0$ is a regular singular point.

 

[Dick]

I would suggest trying a series solution noting $x=0$ is a regular singular point.

I would try some substitutions first. Like maybe u=yx.