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

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 -