# Bessel functions solution

1. Jun 8, 2010

### dats13

*Please remove this post. I reposted in the correct homework section. *

I am trying to solve this equation in terms of Bessel functions.

xy"-y'+(4x^3)y=0

I am sure how to do this. The first thing that comes to mind is to solve for a series solution. This solution can then be compared to the bessel function and from that I can determine the first solution and thus get the second linearly independent solution.

Would this be the correct approach or is there any other way to solve for the general solution in terms of Bessel functions?

Last edited: Jun 8, 2010
2. Jun 14, 2010

### JJacquelin

Hello,

let X = x²
You will easily go to d²y/dX² + y =0
hence y = A cos(X) + B sin(X)
A, B : constant
Solutions : y = A*cos(x²) + B*sin(x²)
Since cos(x²) and sin(x²) are related to Bessel functions of order (1/2) and (-1/2)
y = C*x*J_(1/2)(x²) + D*x*J(-1/2)(x²)
C, D : constant