# Decomposing a 4th order linear differential equation as a symmetric product

• Volume: 58, Issue: 1, page 89-96
• ISSN: 0137-6934

top

## Abstract

top
Let L(y) = 0 be a linear differential equation with rational functions as coefficients. To solve L(y) = 0 it is very helpful if the problem could be reduced to solving linear differential equations of lower order. One way is to compute a factorization of L, if L is reducible. Another way is to see if an operator L of order greater than 2 is a symmetric power of a second order operator. Maple contains implementations for both of these. The next step would be to see if L is a symmetric product of two lower order equations. In this document we will show how to find the formulas needed to solve this problem for the smallest case, where the order of L is 4. This case is already non-trivial; to find the formulas the help of a computer algebra system was needed.

## How to cite

top

Mark van Hoeij. "Decomposing a 4th order linear differential equation as a symmetric product." Banach Center Publications 58.1 (2002): 89-96. <http://eudml.org/doc/281612>.

@article{MarkvanHoeij2002,
abstract = {Let L(y) = 0 be a linear differential equation with rational functions as coefficients. To solve L(y) = 0 it is very helpful if the problem could be reduced to solving linear differential equations of lower order. One way is to compute a factorization of L, if L is reducible. Another way is to see if an operator L of order greater than 2 is a symmetric power of a second order operator. Maple contains implementations for both of these. The next step would be to see if L is a symmetric product of two lower order equations. In this document we will show how to find the formulas needed to solve this problem for the smallest case, where the order of L is 4. This case is already non-trivial; to find the formulas the help of a computer algebra system was needed.},
author = {Mark van Hoeij},
journal = {Banach Center Publications},
keywords = {fouth order linear differential equation; symmetric product; rational functions as coefficients},
language = {eng},
number = {1},
pages = {89-96},
title = {Decomposing a 4th order linear differential equation as a symmetric product},
url = {http://eudml.org/doc/281612},
volume = {58},
year = {2002},
}

TY - JOUR
AU - Mark van Hoeij
TI - Decomposing a 4th order linear differential equation as a symmetric product
JO - Banach Center Publications
PY - 2002
VL - 58
IS - 1
SP - 89
EP - 96
AB - Let L(y) = 0 be a linear differential equation with rational functions as coefficients. To solve L(y) = 0 it is very helpful if the problem could be reduced to solving linear differential equations of lower order. One way is to compute a factorization of L, if L is reducible. Another way is to see if an operator L of order greater than 2 is a symmetric power of a second order operator. Maple contains implementations for both of these. The next step would be to see if L is a symmetric product of two lower order equations. In this document we will show how to find the formulas needed to solve this problem for the smallest case, where the order of L is 4. This case is already non-trivial; to find the formulas the help of a computer algebra system was needed.
LA - eng
KW - fouth order linear differential equation; symmetric product; rational functions as coefficients
UR - http://eudml.org/doc/281612
ER -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.