Geodesic
On one (algebraic) solution of the Euler equations
Matematičeskoe obrazovanie, no. 3 (2022), pp. 15-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {E. M. Arkhipova and V. V. Ivlev and E. A. Krivoshey},
     title = {On one (algebraic) solution of the {Euler} equations},
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E. M. Arkhipova; V. V. Ivlev; E. A. Krivoshey. On one (algebraic) solution of the Euler equations. Matematičeskoe obrazovanie, no. 3 (2022), pp. 15-22. http://geodesic.mathdoc.fr/item/MO_2022_3_a1/

[1] V. V. Ivlev, M. V. Baranova, “Ob odnom klasse lineinykh differentsialnykh uravnenii”, Matematicheskoe obrazovanie, 2012, no. 4 (64), 35–40 | Zbl

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