# Euler Cauchy equation problem

1. Nov 16, 2007

### engineer_dave

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. Nov 16, 2007

### quasar987

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

3. Nov 16, 2007

### HallsofIvy

Staff Emeritus
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.

4. Nov 16, 2007

### Kummer

The characheristic equation here is $$k(k-1)-2=0$$. The solution would then be $$y=c_1|x|^{k_1}+c_2|x|^{k_2}$$ on $$(-\infty,0)\cup (0,\infty)$$.