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We investigate the evolution equation of linear density perturbations in theFriedmann-Robertson-Walker universe with matter, radiation and the cosmologicalconstant. The concept of solvability by quadratures is defined and used toprove that there are no "closed form" solutions except for the known Chernin,Heath, Meszaros and simple degenerate ones. The analysis is performed applyingKovacic's algorithm. The possibility of the existence of other, more generalsolutions involving special functions is also investigated.Comment: 13 pages. The latest version with added references, and a relevant  new paragraph in section I

Nonintegrability of density perturbations in the Friedmann-Robertson-Walker universe