Geodesic
On nonlinear algebraic differential systems reducible to non-degenerate systems of ordinary differential equations. Theory and numerical methods of solution
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 15-21 
Yu. E. Boyarintsev. On nonlinear algebraic differential systems reducible to non-degenerate systems of ordinary differential equations. Theory and numerical methods of solution. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 15-21. http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a1/
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     title = {On nonlinear algebraic differential systems reducible to non-degenerate systems of ordinary differential equations. {Theory} and numerical methods of solution},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider algebraic differential systems of the form $$ \frac{dAx}{dt}=Bx+f(x,t) $$ with a regular pair of matrices $(A,В)$. The conditions of reducibility of such systems to non-degenerate systems of ordinary differential equations (ODE) of first order with respect to the derivative $x'(t)$ are given. Methods for the numerical solution of $x(t)$ are proposed.

[1] Chistyakov V. F., Scheglova A. A., Izbrannye glavy teorii algebro-differentsialnykh sistem, Nauka, Novosibirsk, 2003 | MR | Zbl

[2] Boyarintsev Yu. E., Lineinye i nelineinye algebro-differentsialnye sistemy, Nauka, Novosibirsk, 2000 | Zbl

[3] Boyarintsev Yu. E., Orlova I. V., Puchki matrits i algebro-differentsialnye sistemy, Nauka, Novosibirsk, 2006