Integrability of Planar Polynomial Differential Systems through Linear Differential Equations
Integrability of Planar Polynomial Differential Systems through Linear Differential Equations
In this work, we consider rational ordinary differential equations dy/dx = Q(x,y)/P(x,y), with Q(x,y) and P(x,y) coprime polynomials with real coefficients. We give a method to construct equations of this type for which a first integral can be expressed from two independent solutions of a second-order homogeneous linear differential equation. …