1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Converting 2nd order ODE to Bessel Function

  1. Sep 7, 2008 #1
    1. The problem statement, all variables and given/known data
    I am attempting to solve the 2nd order ODE as follows using the generalized solution to the Bessel's equation

    2. Relevant equations
    original ODE:

    3. The attempt at a solution
    My first thought is to bring out an x^-1 outside of the function so that I end up with:
    I would then solve the resulting Bessel equation found inside the parentheses, and multiply the resulting solution by x^-1. Is this at all a legal operation? Thank you.
  2. jcsd
  3. Sep 7, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    There is no need for the x-1 outside. Just multiply both sides of the original equation by x.
  4. Sep 7, 2008 #3
    Now if the opposite were true and I was trying to drop the power of x's by 1:

    example: (x^3)[tex]d^{2}y[/tex]/[tex]dx^{2}[/tex]+(x^2)dy/dx+(x^3)y=0

    Could I then instead divide by x to come up with:

    with the understanding that the solution to the resulting Bessel function would exclude any results for when x-> 0?
  5. Sep 7, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    Well, because x2 still multiplying the second derivative that would be a problem any way, but you are right if you divided by something that completely got rid of a function multiplying the highest derivative, then you would have to add that condition.
  6. Sep 23, 2010 #5
    Hey I need some help in converting the second order differential equation into..
    I was able to convert the original equation into the following form x^2*y''+2x*y'+x^2*y=0
    I am not able to move forward from here..
    Please could you suggest some method
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Converting 2nd order ODE to Bessel Function
  1. 2nd order ODE (Replies: 20)

  2. 2nd ORDER ODE MIRROR (Replies: 4)