On the symmetry solutions of two-dimensional systems not solvable by   standard symmetry analysis
  A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are linearizable, complex-linearizable and solvable systems. We also present the underlying concept diagrammatically that provides an analogue in $\Re^{3}$ of the geometric linearizability criteria in $\Re^2$. 
Sajid Ali, Asghar Qadir, Muhammad Safdar
math.CA