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!

Euler Cauchy equation problem

  1. Nov 16, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the general solution of x^2y" - 2y = 0

    2. Relevant equations

    3. The attempt at a solution

    Can anyone tell me how to find the general solution of the Euler Cauchy equation. How do we make it into one?? Thanks.
  2. jcsd
  3. Nov 16, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    there is a general method for solving 2nd order ODE of the form y''+f(x)y+g(x)=0 that you can look up in any self respecting book on differential equations. for instance boyce & diprima
  4. Nov 16, 2007 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    Why would you be given the problem of solving an Euler-Cauchy equation if you were told nothing beforehand about solving such a thing?

    Try a "trial solution" of the form y= xr where r is an unknown number.
  5. Nov 16, 2007 #4
    The characheristic equation here is [tex]k(k-1)-2=0[/tex]. The solution would then be [tex]y=c_1|x|^{k_1}+c_2|x|^{k_2}[/tex] on [tex](-\infty,0)\cup (0,\infty)[/tex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Euler Cauchy equation problem
  1. Euler-cauchy equation (Replies: 2)

  2. Euler-Cauchy Problem (Replies: 2)