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

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van Hoeij M.

Banach Center Publications

2002

tom 58

nr 1

89-96

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.

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1 Banach Center Publications

1 van Hoeij M.

1 2002

Wyniki wyszukiwania

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