September 7, 2023 Compiled on September 7, 2023 at 2:33pm

1 Classiﬁcation and integration of ordinary diﬀerential equations
between xy allowing a set of transformations. Sophus Lie (Mathematische
Annalen volume 32, pages 21328 1888)

2 Elementry First Integrals of Diﬀerential equations by M.J.Prelle, M.F. Singer (1983)

3 Solving second order ordinary diﬀerential equations by extending the Prelle-Singer method. by L.G.S. Duarte, da Mota, J,E,F, Skea (2018)

4 Invariants and invariant description of second-order ODEs with three inﬁnitesimal symmetries. I. By Nail H. Ibragimov, Sergey V. Meleshko (2005)

5 Invariants and invariant description of second-order ODEs with three inﬁnitesimal symmetries. II. By Nail H. Ibragimov, Sergey V. Meleshko (2005)

6 On ﬁrst integrals of second-order ordinary diﬀerential equations. By S. V. Meleshko, S. Moyo, C. Muriel, J. L. Romero, P. Guha, A. G. Choudhury (2013)

7 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS AND FIRST INTEGRALS OF THE FORM \(A(t,x)\dot {x}+B(t,x)\) by C. MURIEL, J. L. ROMERO (2009)

8 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS AND FIRST INTEGRALS OF THE FORM \(C(t) + \genfrac {}{}{}{}{1}{(A(t, x)\dot {x} + B(t, x))}\) by C. MURIEL, J. L. ROMERO (2011)

9 Connections between symmetries and integrating factors of ODES (M.S. Thesis) by Theodore Kolokolnikov (1999)

10 On the complete integrability and linearization of certain second-order nonlinear ordinary diﬀerential equations. By V. K. CHANDRASEKAR, M. SENTHILVELAN AND M. LAKSHMANAN (2005)

11 A Simple and Uniﬁed Approach to Identify Integrable Nonlinear Oscillators and Systems. By V. K. Chandrasekar, S. N. Pandey, M. Senthilvelan, and M. Lakshmanan (2018)

12 ALGEBRAIC PROPERTIES OF FIRST INTEGRALS FOR SYSTEMS OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS OF MAXIMAL SYMMETRY. By A. Aslam, K.S. Mahomed and E. Momoniat. (2016)

13 Integrating Factors and First Integrals for Ordinary Diﬀerential Equations. By S.C. Anco and G.W. Bluman. (1997)

14 SYMMETRY AND INTEGRABILITY BY QUADRATURES OF ORDINARY DIFFERENTIAL EQUATIONS. By Artemio GONZALEZ-LOPEZ (1988)

15 Integrating Factors and ODE Patterns. By E.S. Cheb-Terraba, A.D. Rochea (1997)

16 Integrating factors for second order ODEs. By E.S. Cheb-Terraba, A.D. Rochea (1999)

17 Integrating factors, adjoint equations and Lagrangians. By Nail H. Ibragimov (2005)

18 Exactness of Second Order Ordinary Diﬀerential Equations and Integrating Factors. By R. AlAhmad, M. Al-Jararha, H. Almeﬂeh (2014)

19 A New Approach for Solving Second Order Ordinary Diﬀerential Equations. By Laith K. AL-Hwawcha and Namh A. Abid (2008)

20 On Exact Solutions of Second Order Nonlinear Ordinary Diﬀerential Equations. By Amjed Zraiqat, Laith K. Al-Hwawcha (2015)

21 On Solving Some Classes of Second Order ODEs. By R. AlAhmad, M. Al-Jararha (2017)

22 \(\lambda \) symmetry and integrating factors for \(x''( f(t,x)+g(t,x)x') e^x\). By Khodayar Goodarzi and Mehdi Nadjaﬁkhah (2022)

23 On invariants of second-order ordinary diﬀerential equations \(y'' = f(x, y, y')\) via point transformations. By Ahmad Y. Al-Dweik (2014)

24 Invariance of second order ordinary diﬀerential equations under two-dimensional aﬃne subalgebras of ErmakovPinney Lie algebra. By J. F. Carinena, F. Gungor, P. J. Torres (2020)

25 Solutions of Systems of Ordinary Diﬀerential Equations Using Invariants of Symmetry Groups. By Fatma Al-Kindia, Muhammad Ziadb (2019)

26 On the Method of Diﬀerential Invariants for Solving Higher Order Ordinary Diﬀerential Equations. By Winter Sinkala, Molahlehi Charles Kakuli (2020)

27 On the Eight Dimensional Point Symmetries of Second Order Linear O.D.E’s. By Uchechukwu Opara (2020)

28 Review of Symbolic Software for Lie Symmetry Analysis. By W. HEREMAN (1997)

2 Elementry First Integrals of Diﬀerential equations by M.J.Prelle, M.F. Singer (1983)

3 Solving second order ordinary diﬀerential equations by extending the Prelle-Singer method. by L.G.S. Duarte, da Mota, J,E,F, Skea (2018)

4 Invariants and invariant description of second-order ODEs with three inﬁnitesimal symmetries. I. By Nail H. Ibragimov, Sergey V. Meleshko (2005)

5 Invariants and invariant description of second-order ODEs with three inﬁnitesimal symmetries. II. By Nail H. Ibragimov, Sergey V. Meleshko (2005)

6 On ﬁrst integrals of second-order ordinary diﬀerential equations. By S. V. Meleshko, S. Moyo, C. Muriel, J. L. Romero, P. Guha, A. G. Choudhury (2013)

7 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS AND FIRST INTEGRALS OF THE FORM \(A(t,x)\dot {x}+B(t,x)\) by C. MURIEL, J. L. ROMERO (2009)

8 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS AND FIRST INTEGRALS OF THE FORM \(C(t) + \genfrac {}{}{}{}{1}{(A(t, x)\dot {x} + B(t, x))}\) by C. MURIEL, J. L. ROMERO (2011)

9 Connections between symmetries and integrating factors of ODES (M.S. Thesis) by Theodore Kolokolnikov (1999)

10 On the complete integrability and linearization of certain second-order nonlinear ordinary diﬀerential equations. By V. K. CHANDRASEKAR, M. SENTHILVELAN AND M. LAKSHMANAN (2005)

11 A Simple and Uniﬁed Approach to Identify Integrable Nonlinear Oscillators and Systems. By V. K. Chandrasekar, S. N. Pandey, M. Senthilvelan, and M. Lakshmanan (2018)

12 ALGEBRAIC PROPERTIES OF FIRST INTEGRALS FOR SYSTEMS OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS OF MAXIMAL SYMMETRY. By A. Aslam, K.S. Mahomed and E. Momoniat. (2016)

13 Integrating Factors and First Integrals for Ordinary Diﬀerential Equations. By S.C. Anco and G.W. Bluman. (1997)

14 SYMMETRY AND INTEGRABILITY BY QUADRATURES OF ORDINARY DIFFERENTIAL EQUATIONS. By Artemio GONZALEZ-LOPEZ (1988)

15 Integrating Factors and ODE Patterns. By E.S. Cheb-Terraba, A.D. Rochea (1997)

16 Integrating factors for second order ODEs. By E.S. Cheb-Terraba, A.D. Rochea (1999)

17 Integrating factors, adjoint equations and Lagrangians. By Nail H. Ibragimov (2005)

18 Exactness of Second Order Ordinary Diﬀerential Equations and Integrating Factors. By R. AlAhmad, M. Al-Jararha, H. Almeﬂeh (2014)

19 A New Approach for Solving Second Order Ordinary Diﬀerential Equations. By Laith K. AL-Hwawcha and Namh A. Abid (2008)

20 On Exact Solutions of Second Order Nonlinear Ordinary Diﬀerential Equations. By Amjed Zraiqat, Laith K. Al-Hwawcha (2015)

21 On Solving Some Classes of Second Order ODEs. By R. AlAhmad, M. Al-Jararha (2017)

22 \(\lambda \) symmetry and integrating factors for \(x''( f(t,x)+g(t,x)x') e^x\). By Khodayar Goodarzi and Mehdi Nadjaﬁkhah (2022)

23 On invariants of second-order ordinary diﬀerential equations \(y'' = f(x, y, y')\) via point transformations. By Ahmad Y. Al-Dweik (2014)

24 Invariance of second order ordinary diﬀerential equations under two-dimensional aﬃne subalgebras of ErmakovPinney Lie algebra. By J. F. Carinena, F. Gungor, P. J. Torres (2020)

25 Solutions of Systems of Ordinary Diﬀerential Equations Using Invariants of Symmetry Groups. By Fatma Al-Kindia, Muhammad Ziadb (2019)

26 On the Method of Diﬀerential Invariants for Solving Higher Order Ordinary Diﬀerential Equations. By Winter Sinkala, Molahlehi Charles Kakuli (2020)

27 On the Eight Dimensional Point Symmetries of Second Order Linear O.D.E’s. By Uchechukwu Opara (2020)

28 Review of Symbolic Software for Lie Symmetry Analysis. By W. HEREMAN (1997)

These are collection of papers related to ﬁnding integrating factors for higher order diﬀerential equations. Mainly for second order ode’s and higher. As I was studying this subject I thought it will be good idea to have any related paper I ﬁnd on the subject in one place for easy access. The HTML version has only the outlines. Only the PDF version has the actual papers shown.