Writing a Bessel function solution for u'' - bc(x^m)u = 0

[ramtin]

Homework Statement

u''-bc (x^m) u =0

Homework Equations

How can I write the general solution in terms of Bessel function?

The Attempt at a Solution

This form is a transformed vresion of y'+by^2=cx^m with dummy variable by=1/u *du/dx

 

[LCKurtz]

Homework Statement

u''-bc (x^m) u =0

Homework Equations

How can I write the general solution in terms of Bessel function?

The Attempt at a Solution

This form is a transformed vresion of y'+by=cx^m with dummy variable by=1/u *du/dx

I'm curious why you would go to the trouble of transforming your original DE when you can solve it directly. It's just a constant coefficient DE with a non-homogeneous polynomial term.

 

[ramtin]

I'm curious why you would go to the trouble of transforming your original DE when you can solve it directly. It's just a constant coefficient DE with a non-homogeneous polynomial term.

it was y'+by^2=cx^m ,Iforgot to type the y squared power

 

[LCKurtz]

Here is what Maple gives, for what it's worth: