Reduction of underdetermined systems of ordinary differential equations. IV (Q1939465)

The author continues to study underdetermined systems of quasi-linear autonomous ordinary differential equations satisfying a constant rank condition. The current article considers the decomposition of such systems into two subsystems one of which contains less unknown functions than the original one. The analysis is done via the associated Pfaffian system and reduces to the question of finding an integrable codistribution of lower rank satisfying certain conditions. For Part III, see [the author, ibid. 47, No. 11, 1556--1562 (2011); translation from Differ. Uravn. 47, No. 11, 1538--1544 (2011; Zbl 1247.34055)].