5 References

1. Symmetry Methods for Differential Equations. By PETER E. HYDON. CAMBRIDGE UNIVERSITY PRESS. 2000.
2. Symmetry and integration methods for differential equations. By Bluman and Anco. Springer publishing.
3. Introduction to symmetry analysis. By Brian J. Cantwell. See page 158 for table of known \(\xi ,\eta \) per first ode type.
4. 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).
5. Sym Mathematica software package. By Stilianos Dimas and Dimitris Tsoubelis.
6. SymmetryAnalysis Mathematica package. By Brian J. Cantwell.
7. Maple symgen and related commands in the ODEtools package.
8. Computer Algebra Solving of First Order ODEs Using Symmetry Methods. 1996 by Durate, Terrab, Mota. IF-UERJ-27/96
9. The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods by Ruth A. Steinhour, 2013.
10. A practical course in differential equations and Mathematical modeling. By Nail H. Ibragimov. 2010. Chapter 6. Nonlinear ordinary differential equations.
11. Symmetry Analysis of Differential Equations by Daniel J. Arrigo.
12. Many other references, listed in my links page under computer algebra section.