In 1892 he received his agrégation and in 1898 he received his PhD under Paul Tannery at ENS with thesis Essai sur la théorie générale de l'intégration et sur la classification des transcendantes.
[2] In his thesis, Drach developed a Galois theory for differential equations, building upon the work of Émile Picard, Sophus Lie and Ernest Vessiot.
After that he was Maître de Conférences at the University (Faculté des Sciences) in Clermont-Ferrand.
During World War I he studied the mathematical theory of ballistics and published the results of his research around 1920.
In retirement he moved to Cavalaire in southern France, where he had a country estate to which he frequently withdrew because of his health.