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Classification of second order linear ordinary differential equations with rational coefficients. (English) Zbl 1422.34127

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.

MSC:

34C14 Symmetries, invariants of ordinary differential equations
34A30 Linear ordinary differential equations and systems
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