A+ CATEGORY SCIENTIFIC UNIT

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

Volume 58 / 2002

Mark van Hoeij Banach Center Publications 58 (2002), 89-96 MSC: Primary 34-04; Secondary 34A30 DOI: 10.4064/bc58-0-8

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.

Authors

  • Mark van HoeijDepartment of Mathematics
    Florida State University
    Tallahassee, FL 32306-3027, U.S.A.
    e-mail

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