Abstract
This paper presents a simple and efficient method for determining the rational solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation , is reducible, we look for the rational solutions of Riccati differential equation , by reducing the number of checks to be made and by accelerating the search for the partial fraction decomposition of the solution reserved for the poles of which are false poles of . This partial fraction decomposition of solution can be used to code . The examples demonstrate the effectiveness of the method.
Highlights
The quadratic Riccati differential equation: ER : σ p2σ2 p1σ p0, 1.1 where p0, p1, and p2 are in a differential field Ã, p2 / 0
The quadratic Riccati differential equation is first converted to a reduced Riccati differential equation: Er : θ θ2 r, 1.2 where θ −p2σ − 1/2 a, with a p2/p2 p1 and r 1/4 a2 − 1/2 a − p2p0
We put y /y θ, reduced Riccati differential equation 1.2 is converted to a second-order linear ordinary differential equation
Summary
The quadratic Riccati differential equation: ER : σ p2σ2 p1σ p0, 1.1 where p0, p1, and p2 are in a differential field à , p2 / 0. In case the differential Galois group of the differential equation El : y ry, r ∈ x is reducible, we look for the rational solutions of Riccati differential equation θ θ2 r, by reducing the number of checks to be made and by accelerating the search for the partial fraction decomposition of the solution reserved for the poles of θ which are false poles of r. This partial fraction decomposition of solution can be used to code r.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
