Symmetries and Integrating Factors
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Cheb-Terrab and Roche (J. Sym. Comp. 27 (1999), 501519) presented what they termed a systematic algorithm for the construction of integrating factors for second order ordinary differential equations. They showed that there were instances of odinary differential equations without Lie point symmetries which were solvable with this algorithm. We demonstrate that the existence of integrating factors is paralleled by the existence of suitable Lie symmetries which enable one to reduce the equations to quadratures thereby emphasising the fact that integrability relies upon symmetry.
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TY - JOUR AU - P.G.L. Leach AU - S.É. Bouquet PY - 2002 DA - 2002/09/02 TI - Symmetries and Integrating Factors JO - Journal of Nonlinear Mathematical Physics SP - 73 EP - 91 VL - 9 IS - Supplement 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2002.9.s2.7 DO - 10.2991/jnmp.2002.9.s2.7 ID - Leach2002 ER -