Solving 1ODEs with functions

TL;DR

This paper introduces a new, more efficient method for solving first order ordinary differential equations using functions, building on previous theoretical work within the extended Prelle-Singer framework.

Contribution

It presents a novel approach to solving 1ODEs that improves efficiency and applicability compared to prior methods, especially for equations involving parameters.

Findings

Enhanced method increases solving efficiency for many 1ODEs

Applicable to problems with parameters influencing rates of change

Builds on extended Prelle-Singer theoretical framework

Abstract

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background to deal, in the extended Prelle-Singer approach context, with systems of 1ODEs. In this present paper, we will apply these results in order to produce a method that is more efficient in a great number of cases. Directly, the solving of 1ODEs is applicable to any problem presenting parameters to which the rate of change is related to the parameter itself. Apart from that, the solving of 1ODEs can be a part of larger mathematical processes vital to dealing with many problems.