Cauchy-Euler Differential Equations (or equidimensional equations) are differential equations in the form:
The defining factor of Cauchy-Euler equations is that the degree of the coefficient is equal to the order of the derivative. Because of this the solutions we used to solve homogeneous linear differential equations won't work.
See W3L2 - Cauchy-Euler Differential Equations and Chapter 4.7 - Cauchy-Euler Equations for more information and examples.