Symmetries of Ordinary Differential Equations

Gerd Baumann
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Gerd Baumann: University of Ulm, Department of Mathematical Physics

Chapter 4 in Symmetry Analysis of Differential Equations with Mathematica®, 2000, pp 96-215 from Springer

Abstract: Abstract Let us start with the following question. Suppose you have to solve an ordinary differential equation of second order like $$\begin{gathered} equation1 = {\partial _{(x,2)}}u[x]\left( {x - u[x]} \right){\partial _x}u[x] = = 0; \hfill \\ equation1//LieTradionalForm \hfill \\ - ( - u + x){u_x} + {u_{x,x}} = = 0 \hfill \\ \end{gathered} $$ .

Keywords: Ordinary Differential Equation; Vector Field; Riccati Equation; Canonical Variable; Invariance Condition (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-2110-4_4

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