Setting the DE becomes the algebraic equation in m...
... because the 'common term' can be 'canceled'. If and are [distinct] solutions of (1), then the solution of the DE will be...
A second order homogeneous Cauchy-Euler Equation is an equation of the type:
, a,b,c constants,
Explain why, in the case of the homogeneous C-E DE, a solution can be of the form
It makes sense that that is the correct Ansatz, but I cannot explain why exactly that should be the case.
And, in fact, for exactly the same reason. The substitution t= ln(x) changes an Euler-Cauchy equation into an equation with constant coefficients.