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.
