On the integrability of differential equations by quadratures according to Maximovič. (Q596254)

In the late 19th century, Vladimir Maximovič developed a theory of the integrability of ordinary differential equations by quadratures which has been more or less forgotten by now. The author intends to present in the article a rigorous form of Maximovič's definition of integrability by quadratures and to prove that all first-order ordinary differential equations integrable in this sense are linearisable by a transformation of the dependent variable. The article concludes with a brief account of Maximovič's life.