Linearizability Criteria for a Class of Third Order Semi-Linear Ordinary Differential Equations
نویسندگان
چکیده
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a class of third order semi-linear ordinary differential equations, which is distinct from the classes available in the literature. Some examples are given and discussed.
منابع مشابه
Conditional Linearizability Criteria for Scalar Fourth Order Semi-Linear Ordinary Differential Equations
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating the third order equation. This yields criteria for linearizability of a class of fourth order semi-linear ordinary differential equations, which have not bee...
متن کاملInequivalence of Classes of Linearizable Systems of Second Order Ordinary Differential Equations Obtained by Real and Complex Symmetry Analysis
Linearizability criteria for systems of two cubically semi-linear second order ordinary differential equations (ODEs) were obtained by geometric means using real symmetry analysis (RSA). Separately, complex symmetry analysis (CSA) was developed to provide means to discuss systems of two ODEs. It was shown that CSA provides a class of linearizable systems of two cubically semi-linear ODEs. Linea...
متن کاملGeometric Linearization of Ordinary Differential Equations
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable equations and even on systems of equations. However, little has been done in the way of providing explicit criteria to determine their linearizability. Using...
متن کاملN ov 2 00 7 Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - I : Ordinary Differential Equations
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of two real ordinary differential equations. The transformations that map a system of two nonlinear ordinary differential equations into systems of linear ordin...
متن کاملOn Linearization by Generalized Sundman Transformations of a Class of Liénard Type Equations and Its Generalization
We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...
متن کامل