Geodesic
Particular integrals of systems of ordinary differential equations
Sbornik. Mathematics, Tome 75 (1993) no. 2, pp. 353-369

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For systems of ordinary differential equations, the concept of particular integral is extended, enabling one to find several approaches to constructing the first integral and the last Jacobi multiplier. Methods are developed for distinguishing a center and focus, and for finding limit cycles of systems having particular algebraic integrals, taking their weight into account, and of systems having conditional particular integrals. 
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     author = {V. N. Gorbuzov and V. Yu. Tyshchenko},
     title = {Particular integrals of systems of ordinary differential equations},
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V. N. Gorbuzov; V. Yu. Tyshchenko. Particular integrals of systems of ordinary differential equations. Sbornik. Mathematics, Tome 75 (1993) no. 2, pp. 353-369. http://geodesic.mathdoc.fr/item/SM_1993_75_2_a3/