1. ## Bessel function

The solution of the initial value problem
(x^2)y'' +xy'+(x^2)y = 0 y(0)=1 y'(0)= 0

is called a Bessel function function of order 0

Solve the initial value problem to find a power series expansion for the Bessel function

2. Originally Posted by Csou090490
The solution of the initial value problem
(x^2)y'' +xy'+(x^2)y = 0 y(0)=1 y'(0)= 0

is called a Bessel function function of order 0

Solve the initial value problem to find a power series expansion for the Bessel function

Say x>0.

Since LaTeX is down and I do not want to solve this by posting math codes. And further this is an irregular point at the center of the series, we need to use the Frobenius method which takes much longer. I will just give you the answer.

(I gave you the general solution for x>0 yet in your initial value problem you gave x=0. That is a problem, maybe you meant something else).