3 papers
math-ph2024
A Linear Prelle-Singer method
L. G. S. Duarte, H. S. Ferreira, L. A. C. P. da Mota
The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of…
nlin.CD2023
A new use of nonlocal symmetries for computing Liouvillian first integrals of rational second order ordinary differential equations
I. Deme, L. G. S. Duarte, L. A. C. P. da Mota
Here we present an efficient method for finding and using a nonlocal symmetry admitted by a rational second order ordinary differential equation (rational 2ODE) in order to find a…
math-ph2023
Solving first order differential equations presenting elementary functions
L. G. S. Duarte, L. A. C. P. da Mota, A. B. M. M. Queiroz
We have already dealt with the problem of solving First Order Differential Equations (1ODEs) presenting elementary functions before in [1, 2]. In this present paper, we have establ…