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Homework Help: 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


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    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


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    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].
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