Abstract
We discuss the linearization problem of third-order ordinary differential equation under the generalized linearizing transformation. We identify the form of the linearizable equations and the conditions which allow the third-order ordinary differential equation to be transformed into the simplest linear equation. We also illustrate how to construct the generalized linearizing transformation. Some examples of linearizable equation are provided to demonstrate our procedure.
Highlights
There has been major interest in the nonlinear problems, since most equations are inherently nonlinear in nature
We identify the form of the linearizable equations and the conditions which allow the third-order ordinary differential equation to be transformed into the simplest linear equation
It is of interest to provide general criteria for the linearizability of nonlinear ordinary differential equations, as they can be reduced to solvable equations
Summary
There has been major interest in the nonlinear problems, since most equations are inherently nonlinear in nature. In [6], Nakpim and Meleshko pointed out that the solution of the linearization problem for a second-order ordinary differential equation via the generalized Sundman transformation considered earlier by Duarte et al [3] using the Laguerre form is not complete. The linearization problem for a third-order ordinary differential equation was investigated with respect to a generalized Sundman transformation [7, 8]. The generalized Sundman transformation was applied for obtaining necessary and sufficient conditions for a third-order ordinary differential equation to be equivalent to a linear equation in the Laguerre form [6]. The linearization problem of a fourth-order ordinary differential equation with respect to generalized Sundman transformations was studied in [11].
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