arXiv subjects
Publications and source records attributed to N. Euler.
We compute invariants for the two-variable M\"obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation.
We define a proper differential sequence of ordinary differential equations and introduce a method to derive an alternative sequence of integrals for such a sequence. We describe some general properties which are illustrated by several examples.
We calculate in detail the conditions which allow the most general third order ordinary differential equation to be linearised in X'''(T)=0 under the transformation X(T)=F(x,t), dT=G(x,t)dt. Further generalisations are considered.