Elementary solutions of differential equations

Michael Singer

Vol. 59 (1975), No. 2, 535–547

DOI: 10.2140/pjm.1975.59.535

Abstract

In this paper we deal with the problem: when does a differential equation have an elementary solution, that is a solution which can be expressed in terms of algebraic operations, logarithms and exponentials? As an application of our theorem, we give necessary and sufficient conditions for a certain class of first order differential equations to have elementary solutions.

Mathematical Subject Classification 2000

Primary: 12H05

Milestones

Received: 2 April 1975

Revised: 15 July 1975

Published: 1 August 1975