The connection of Monge-Bateman equations with ordinary differential equations and their generalisation

Abstract

It is shown that the Monge equation is equivalent to the ordinary differential equation $\ddot{X}=0$ of free motion. Equations of Monge type (with their general solutions) are connected with each ordinary differential equation of second order $\ddot{X}=F(\dot{X},X;t)$, integrable by quadratures. The result is generalised to a system of equations of the second order, which is in one to one correspondence with the multidimensional Monge-Bateman system.

LaTeX, 6 pages