论文标题
在沃恩斯基涉及的微分方程的侧面条件下
On a Side Condition for Wronskian-Involving Differential Equations
论文作者
论文摘要
本文的目的是建立在差异几何形状中发生的特定概念和微分方程理论之间建立一些联系，目的是确定一类有趣的不确定的非线性非线性普通微分方程，这些方程满足其解决方案满足由均质的三阶线性普通差异方程组成的特定侧面条件。提出了一种基于提议的侧条件解决此类的wronskian涉及微分方程的方法。在空间曲线理论中产生的tzitzeica曲线方程被视为一个例子，并获得了该方程的新的封闭式和积分形式的解决方案。
The purpose of this paper is to make a few connections among specific concepts occurring in differential geometry and the theory of differential equations with the aim of identifying an intriguing class of undetermined nonlinear ordinary differential equations whose solutions satisfy a specific side condition consisting in a homogeneous third-order linear ordinary differential equation. A method for solving this class of Wronskian-involving differential equations based on the proposed side condition is presented. The Tzitzeica curve equation arising in the theory of space curves is considered as an example, and new closed and integral-form solutions for this equation are obtained.
