  This paper is centred on solving differential equations by symmetry groups
for first order ODEs and is in response to Starrett (2007). It also explores
the possibility of averting the assumptions by Olver (2000) that, in practice
finding the solutions of the linearized symmetry condition is usually a much
more difficult problem than solving the original ODE but, by inspired guesswork
or geometric intuition, it is possible to ascertain a particular solution of
the linearized symmetry condition. In addition, there is the verification of
the connection between prolongation and the linearized symmetry condition as
used in solving first order ODEs.
