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Chin. Phys. B, 2008, Vol. 17(3): 822-824    DOI: 10.1088/1674-1056/17/3/015
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Noether's and Poisson's methods for solving differential equation $x_s^{\left( m \right)} = F_s \left({t,x_k^{\left( {m - 2} \right)} ,x_k^{\left( {m - 1} \right)} } \right)$

He Guang(何光)a) and Mei Feng-Xiang(梅凤翔)b)
a School of Aerospace Science and Engineering, Beijing Institute of Technology, Beijing 100081, China; b School of Science, Beijing Institute of Technology, Beijing 100081, China
Abstract  This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether method and the Poisson method. Then the solution of the higher-order equation can be obtained by integrating the solution of the second-order equation.
Keywords:  Noether's method      Poisson's method      higher order ordinary differential equation      integration  
Received:  10 August 2007      Accepted manuscript online: 
PACS:  02.30.Hq (Ordinary differential equations)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10572021) and Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022).

Cite this article: 

He Guang(何光) and Mei Feng-Xiang(梅凤翔) Noether's and Poisson's methods for solving differential equation $x_s^{\left( m \right)} = F_s \left({t,x_k^{\left( {m - 2} \right)} ,x_k^{\left( {m - 1} \right)} } \right)$ 2008 Chin. Phys. B 17 822

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