Linearization of third-order ordinary differential equations by generalized Sundman transformations: The case [formula omitted

Abstract

Necessary and sufficient conditions which allow the most general third-order ordinary differential equation x ‴ = f ( t , x , x ′ , x ″ ) to be transformed to X ‴ + α X = 0 under the generalized Sundman transformation X = F ( t , x ) , dT = G ( t , x ) dt , ( F x G ≠ 0 ) , are obtained in the paper. Here α ≠ 0 is constant.