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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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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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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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