Solving Second Order Linear Differential Equations via Algebraic Invariant Curves (original) (raw)

The paper presents a novel approach to solving second-order linear differential equations using algebraic invariant curves. Building on the foundational work of Darboux and the extensions by Prelle and Singer, the proposed method leverages differential Galois theory and the Prelle-Singer algorithm to find elementary first integrals of differential equations. Specific examples demonstrate the applicability and effectiveness of this approach in deriving closed-form solutions, thereby providing a valuable tool for researchers in the fields of mathematics and engineering.