Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe ...

We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals ...

This course continues the study of differential equations. Power series solutions around regular singular points including Bessel equations are presented. First order linear systems and their general ...

The aim of this unit is to introduce the basic theory of ordinary differential equations (ODEs). Ordinary differential equations are very important in applied mathematics. Many phenomena from physics, ...

Abstract: Large language models have demonstrated exceptional performance across various natural language processing tasks. However, their reliance on unstructured text corpora for pre-training limits ...