A second order homogeneous Cauchy-Euler Equation is an equation of the type:

$\displaystyle ax^2y''(x) + bxy'(x) + cy(x) = 0$, a,b,c constants, $\displaystyle x > 0$

Explain why, in the case of the homogeneous C-E DE, a solution can be of the form $\displaystyle y = x^m$

It makes sense that that is the correct Ansatz, but I cannot explain why exactly that should be the case.