Elastic Order Reduction Transformation and Its Application in Solving a
Class of Third-order Nonlinear Differential Equations
Abstract
Based on the theoretical knowledge of elasticity, this paper introduces
elasticity (i.e. elastic transformation) as a tool to solve differential
equations for the first time, and takes a class of third-order nonlinear
ordinary differential equations as an example. First, elastic
transformation is used to reduce the order to second-order solvable
differential equation. Second, by using the elastic inverse
transformation, the analytical solutions of the original equation are
obtained. Finally, the steps of the elastic reduction transformation
method are summarized. The examples show that some nonlinear equations
can be transferred into linear equations, and this method has
theoretical and applied value which is extensive and in-depth.