Geodesic
On one (algebraic) solution of the Euler equations
Matematičeskoe obrazovanie, Tome 103 (2022) no. 3, pp. 15-22.

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In previous papers, a generalization of the well-known Euler equation with an arbitrary differentiable generating function was proposed. Criteria are formulated that allow direct integration of inhomogeneous equations, bypassing the well-known Lagrange method of variation of arbitrary constants. The disadvantage of the method is the necessity of $n$-fold integration of the equation. The present paper considers the idea of replacing the $n$-fold integration with a system of linear equations obtained by a single integration of the original $n$-order equation with the found roots of the characteristic equation. 
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E. M. Arkhipova; V. V. Ivlev; E. A. Krivoshey. On one (algebraic) solution of the Euler equations. Matematičeskoe obrazovanie, Tome 103 (2022) no. 3, pp. 15-22. http://geodesic.mathdoc.fr/item/MO_2022_103_3_a1/

[1] V. V. Ivlev, M. V. Baranova, “Ob odnom klasse lineinykh differentsialnykh uravnenii”, Matematicheskoe obrazovanie, 2012, no. 4 (64), 35–40 <ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1302.86017'>1302.86017</ext-link>

[2] V. V. Ivlev, Matematicheskii analiz. Izbrannoe, AO “Izdatelstvo IKAR”, M., 2018