Geodesic
Generalized solutions of the differential first-order equation with the special rational coefficient
Problemy fiziki, matematiki i tehniki, no. 1 (2021), pp. 54-61

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Solutions in the space of generalized functions of a linear first-order differential equation in which the coefficient is the generalized function generated by the rational function $\frac{2x-a}{x^2-ax}$, $a>0$ are considered. Conditions for the existence of a generalized solution to the Cauchy problem are found. It is shown that the generalized solution does not exist for all considered coefficients.
Keywords: generalized functions, differential equation with generalized coefficient, analytical representation. 
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     author = {E. V. Kuzmina},
     title = {Generalized solutions of the differential first-order equation with the special rational coefficient},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {54--61},
     publisher = {mathdoc},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2021_1_a8/}
}
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E. V. Kuzmina. Generalized solutions of the differential first-order equation with the special rational coefficient. Problemy fiziki, matematiki i tehniki, no. 1 (2021), pp. 54-61. http://geodesic.mathdoc.fr/item/PFMT_2021_1_a8/