Riccati-parameter solutions of nonlinear second-order ODEs
Rosu Barbus, Haret-Codratian
It has been proven by Rosu and Cornejo-Pe´rez [1, 2] that for some nonlinear second-order ODEs it is a very simple task to ﬁnd one particular solution once the nonlinear equation is factorized with the use of two ﬁrst-order diﬀerential operators. Here, it is shown that an interesting class of parametric solutions are easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a ‘growth’ parameter from the trivial null solution up to the particular solution found through the factorization procedure.