galois theory, :12 Field theory and polynomials::12H Differential and difference algebra [Classificació AMS], Àlgebra diferencial, Galois theory, Lienard equation, Poincare problem, darboux integrating factors, Differential Galois theory, POINCARE PROBLEM, Differential Galois Theory, Liouvillian solution, Rational first integral, GALOIS THEORY, invariant algebraic-curves, INVARIANT ALGEBRAIC-CURVES, Riccati equation, Liénard Equation, SYSTEMS, Integrating factor, multiplicity, LINEAR-DIFFERENTIAL EQUATIONS, :32 Several complex variables and analytic spaces::32S Singularities [Classificació AMS], rational first integral, DARBOUX INTEGRATING FACTORS, Galois, Teoria de, 1st integrals, foliations, Àrees temàtiques de la UPC::Matemàtiques i estadística, inverse problems, MULTIPLICITY, :Matemàtiques i estadística [Àrees temàtiques de la UPC], linear-differential equations, 1ST INTEGRALS, poincare problem, FOLIATIONS, Algebra, integrating factor, Equacions diferencials lineals, Darboux theory of integrability, systems, Differential equations, Linear, Darboux theory of Integrability, Poincaré problem, INVERSE PROBLEMS