The connection of Monge-Bateman equations with ordinary differential equations and their generalisation
A. N. Leznov
Abstract
It is shown that the Monge equation is equivalent to the ordinary differential equation X=0 of free motion. Equations of Monge type (with their general solutions) are connected with each ordinary differential equation of second order X=F( 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.
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