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.