ABSTRACT
As stated in Section 1.4 (see also Dickson [1924], Ovsiannikov [1962], Olver [1986], Bluman and Kumei [1989], Stephani [1989], and Ibragimov [1989a], [1991]), a one-dimensional symmetry algebra can be used to reduce by one the order of a second-order equation. So it is natural to expect that given a two-dimensional algebra the order can be reduced twice, which means we have integrated the equation.
