Express solution as bessel function

Kazz81
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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!
 
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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?
 
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)..
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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