Classification of second order linear ordinary differential equations with rational coefficients (Q2003095)

This work is devoted to second order linear differential equations \(y^{\prime \prime }+A(z)y^{\prime }+B(z)y=0\) with rational coefficient functions \(A, B\). By computing the symmetry group and the generators of the field of differential invariants a classification of this class of equations is obtained. Five examples are discussed with their associated pictures.