  Symmetry analysis of Ramanujan's system of differential equations is
performed by representing it as a third-order equation. A new system consisting
of a second-order and a first-order equation is derived from Ramanujan's
system. The Lie algebra of the new system is equivalent to the algebra of the
third-order equation. This forms the basis of our intuition that for a system
of first-order odes its infinite-dimensional algebra of symmetries contains a
subalgebra which is a representation of the Lie algebra for any system or
differential equation which can be obtained from the original system, even
though the transformations are not point.
