Gunther Reißig and Holger Boche.
A Normal Form for Implicit Differential Equations Near Singular Points.
Proc. 1997 Europ. Conf. on Circuit Th. and Design (ECCTD), Budapest, Hu., Aug. 30-Sept. 3, 1997, vol. 2, 1048-1053.
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We consider differential equations A(x)x'=g(x), where A is a (n x n)-matrix of C1-functions and g is C1. We investigate the above differential equation about singular points x0 that are standard in the sense of Rabier. In particular, the null space of A(x0) is of dimension 1. We show that there is a C1-diffeomorphism that transforms the above equation about x0 into
x1 x1' = +/-1,
x2' = ... = xn' = 0
about 0.

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