  There exist sound literature and algorithms for computing Liouvillian
solutions for the important problem of linear ODEs with rational coefficients.
Taking as sample the 363 second order equations of that type found in Kamke's
book, for instance, 51 % of them admit Liouvillian solutions and so are
solvable using Kovacic's algorithm. On the other hand, special function
solutions not admitting Liouvillian form appear frequently in mathematical
physics, but there are not so general algorithms for computing them. In this
paper we present an algorithm for computing special function solutions which
can be expressed using the 2F1, 1F1 or 0F1 hypergeometric functions. The
algorithm is easy to implement in the framework of a computer algebra system
and systematically solves 91 % of the 363 Kamke's linear ODE examples
mentioned.
