Monge-Bateman方程与常微分方程的联系及其推广
The connection of Monge-Bateman equations with ordinary differential equations and their generalisation
摘要：
证明了Monge方程等价于自由运动的常微分方程$\ddot X=0$。Monge型方程（及其通解）与每个二阶$\ddot X=F(\dot X,X; t)$常微分方程相联系，可通过求积积分。结果被推广到一个系统的二阶方程，这是在一个对应的多维Monge-Bateman系统。
英文摘要：
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.
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