A Maple procedure based on λ-symmetries for second-order ordinary differential equations

摘要

We present a Maple procedure to classify and solve the equations in the class of the 2nd-order ordinary differential equations that admit first integrals that are polynomials of the first degree in the first order derivative. Computational methods based on the theory of -symmetries permit to obtain the integrating factors, the first integrals, the related -symmetries and, if possible, the general solution. The procedure also provides the local and the generalized Sundman transformations that linearize the equations in the class .