Express solution as bessel function

[Kazz81]

Hi Guys, I'm an undergrad student...and i have a difficulty trying to solve

4xy" + 4y' + y = 0, and express the solution in term of Bessel function.

I have tried Frobenius method...then...it didn't work..and I'm really confused

Could anyone please help me with this?...i'd would really appreciate!

 

[HallsofIvy]

Bessel fuinctions are defined as solutions to Bessel's equation.

What is Bessel's equation?

Can you, perhaps by changing varables, change your equation to Bessel's equation?

 

[Kazz81]

Even if I multiply x thru, then divide 4 thru...i still don't get (x^2)y...hmmm..(i.e. Bessel eqn order of zero)..