1999/06/02 by Karl Michael Schmidt, Schmidt, Karl Michael
Mathematics · #01A70 #34A05 #34A46 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods for differential equations #math.CA #msc:01A70 #msc:34A05 #msc:34A46
paper · pdf · doi:10.48550/arxiv.math/9906013
24 pages
arxiv created 1999/06/02 · openalex publication_date 1999/06/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a definition of integration by quadratures of first-order ordinary differential equations, and recover a little known result by Maximovic which states that a first-order ordinary differential equation can be integrated by quadratures only if it arises from the linear equation by a diffeomorphic transformation of the dependent variable. In the appendix this result is applied to the linear second-order equation in a restricted setting. A brief outline of Maximovic's life is also included.