- Kovacic algorithm for differential equations of the type

where are polynomials in (implemented in Macsyma)

- Singer algorithm for differential equations of the type

where are rational or algebraic functions (not implemented until now due to its massive complexity)

- algorithms that look for Liouville type solutions (i.e.,
rational functions extended by algebraic functions, exponential
functions and integrals) or decide if such a solution exists
- examples

Richard Liska