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Collection of papers related to finding integrating factors and first integrals for second and higher order differential equations

Nasser M. Abbasi

January 19, 2025   Compiled on January 19, 2025 at 4:32pm

Contents

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) dotx +B(t,x) by C. MURIEL, J. L. ROMERO (2009)
8 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS AND FIRST INTEGRALS OF THE FORM C(t) + 1/(A(t, x) dotx + 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)
29 Computing closed form solutions of first oder ODEs using the Prelle-Singer procedure. By YIU-KWONG MAN (1993)

  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. These papers also includes ones on Prelle-Singer algorithm.

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) dotx +B(t,x) by C. MURIEL, J. L. ROMERO (2009)

8 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS AND FIRST INTEGRALS OF THE FORM C(t) + 1/(A(t, x) dotx + 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)

29 Computing closed form solutions of first oder ODEs using the Prelle-Singer procedure. By YIU-KWONG MAN (1993)