TITLE:
The Riccati Equation, Differential Transform, Rational Solutions and Applications
AUTHORS:
Malick Ndiaye
KEYWORDS:
Riccati Equation, Differential Transform, Rational Solutions
JOURNAL NAME:
Applied Mathematics,
Vol.13 No.9,
September
30,
2022
ABSTRACT: In this article, the Riccati Equation is considered. Various techniques of finding analytical solutions are explored. Those techniques consist mainly of making a change of variable or the use of Differential Transform. It is shown that the nonconstant rational functions whose numerator and denominator are of degree 1, cannot be solutions to the Riccati equation. Two applications of the Riccati equation are discussed. The first one deals with Quantum Mechanics and the second one deal with Physics.