Symmetry Methods for Differential Equations. By PETER E. HYDON.
CAMBRIDGE UNIVERSITY PRESS. 2000.
Symmetry and integration methods for differential equations. By Bluman and
Anco. Springer publishing.
Introduction to symmetry analysis. By Brian J. Cantwell. See page 158 for table
of known \(\xi ,\eta \) per first ode type.
Using Lie Symmetry to solve first and second order Linear Differential Equation.
Int. J. Adv. Appl. Math. andMech. 7(4) (2020) 91 – 99 (ISSN: 2347-2529).
Sym Mathematica software package. By Stilianos Dimas and Dimitris Tsoubelis.
SymmetryAnalysis Mathematica package. By Brian J. Cantwell.
Maple symgen and related commands in the ODEtools package.
Computer Algebra Solving of First Order ODEs Using Symmetry Methods. 1996
by Durate, Terrab, Mota. IF-UERJ-27/96
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry
Methods by Ruth A. Steinhour, 2013.
Many other references, listed in my links page under computer algebra section.