Integration of an arbitrary linear ODE

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Gibson, Peter C.
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917172081590272
author Gibson, Peter C.
author_facet Gibson, Peter C.
contents The standard text book theory of ODEs lacks a general method to solve linear equations having variable coefficients, providing instead a collection of special techniques for particular classes of equations. The present article addresses this shortcoming in the basic theory. We introduce the multex integral operator, generalizing to several input functions the standard exponential primitive operator that is inverse to the logarithmic derivative. The multex operator serves to integrate in explicit form an arbitrary linear ordinary differential equation.
format Preprint
id arxiv_https___arxiv_org_abs_2512_22344
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Integration of an arbitrary linear ODE
Gibson, Peter C.
Classical Analysis and ODEs
34A05
The standard text book theory of ODEs lacks a general method to solve linear equations having variable coefficients, providing instead a collection of special techniques for particular classes of equations. The present article addresses this shortcoming in the basic theory. We introduce the multex integral operator, generalizing to several input functions the standard exponential primitive operator that is inverse to the logarithmic derivative. The multex operator serves to integrate in explicit form an arbitrary linear ordinary differential equation.
title Integration of an arbitrary linear ODE
topic Classical Analysis and ODEs
34A05
url https://arxiv.org/abs/2512.22344