Geodesic
Integrable ordinary differential equations on free associative algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 88-101

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We consider a classification problem for integrable nonlinear ordinary differential equations with an independent variable belonging to a free associative algebra $\mathcal M$. Every equation of this type admits an $m\times m$ matrix reduction for an arbitrary $m$. The existence of symmetries or first integrals belonging to $\mathcal M$ is used as an integrability criterion. 
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     title = {Integrable ordinary differential equations on free associative algebras},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a7/}
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A. V. Mikhailov; V. V. Sokolov. Integrable ordinary differential equations on free associative algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 88-101. http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a7/