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- W2078166779 abstract "We apply the method of preliminary group classification to ordinary differential equations of the form<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mi mathvariant=normal>'</mml:mi><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant=normal>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>),</mml:mo><mml:mi mathvariant=normal /><mml:mi mathvariant=normal /><mml:mi mathvariant=normal /><mml:mi mathvariant=normal /><mml:mi> i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=normal>0</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>.</mml:mo></mml:math>We show how this method can be implemented via the popular symmetry analysis package PROGRAM LIE provided that the package is supplemented with a small file. We then apply this method to an extension of the generalised Emden-Fowler equation given by<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>′</mml:mi><mml:mi>′</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>=<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup><mml:mfenced separators=|><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>." @default.
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- W2078166779 date "2013-01-01" @default.
- W2078166779 modified "2023-09-27" @default.
- W2078166779 title "Symbolic Implementation of Preliminary Group Classiffication for Ordinary Differential Equations" @default.
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- W2078166779 doi "https://doi.org/10.1155/2013/976271" @default.
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