| Abstract: |
| In this talk a few connections among specific concepts occurring in differential geometry and the theory of differential equations are emphasized. The aim of this work is to identify 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. |
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